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#33 by Bruno Berselli at Thu Aug 18 10:20:15 EDT 2022
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#32 by Joerg Arndt at Thu Aug 18 10:15:50 EDT 2022
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#31 by Seiichi Manyama at Thu Aug 18 10:12:17 EDT 2022
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#30 by Seiichi Manyama at Thu Aug 18 09:49:38 EDT 2022
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| PROG
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(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\2, (2*j+1)!/j!*binomial(i-1, 2*j)*v[i-2*j])); v; \\ Seiichi Manyama, Aug 18 2022
(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)^k/(k!*(n-2*k)!)); \\ Seiichi Manyama, Aug 18 2022
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#29 by Seiichi Manyama at Thu Aug 18 08:36:03 EDT 2022
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(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\2, (2*j+1)!/()!/j)!*!*binomial(i-1, 2*j)*v[i-2*j])); v; \\ Seiichi Manyama, Aug 18 2022
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#28 by Seiichi Manyama at Thu Aug 18 08:35:00 EDT 2022
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(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\2, (2*j+1)!/(j)!*binomial(i-1, 2*j)*v[i-2*j])); v; ; \\ _Seiichi Manyama_, Aug 18 2022
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#27 by Seiichi Manyama at Thu Aug 18 08:33:53 EDT 2022
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| NAME
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EExpansion of e.g.f. exp( x * exp(x^2) ).
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| PROG
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(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\2, (2*j+1)!/(j)!*binomial(i-1, 2*j)*v[i-2*j-1+1])); v;
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#26 by Seiichi Manyama at Thu Aug 18 08:33:24 EDT 2022
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| PROG
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(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\2, (2*j+1)!/(j)!*binomial(i-1, 2*j)*v[i-2*j-1+1])); v;
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| STATUS
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approved
editing
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#25 by Vaclav Kotesovec at Fri Aug 08 04:40:51 EDT 2014
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#24 by Vaclav Kotesovec at Fri Aug 08 04:40:28 EDT 2014
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| LINKS
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Vaclav Kotesovec, <a href="/A216688/a216688.pdf">Asymptotic solution of the equations using the Lambert W-function</a>
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| STATUS
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approved
editing
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