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#13 by Michael De Vlieger at Sun Feb 26 08:42:38 EST 2023
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#12 by Joerg Arndt at Sun Feb 26 06:56:21 EST 2023
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#11 by Seiichi Manyama at Sun Feb 26 06:44:35 EST 2023
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#10 by Seiichi Manyama at Sun Feb 26 06:39:34 EST 2023
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| NAME
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Expansion of e.g.f. Sum_{k>=0} exp((4^k- - 1)*x) * x^k/k!.
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#9 by Seiichi Manyama at Sun Feb 26 02:20:00 EST 2023
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1, 1, 7, 73, 1711, 75121, 6743287, 1169659513, 412296162271, 284887781497441, 400134611520973927, 1108533158650520901673, 6238465090832886119430031, 69421876683500992783472318161, 1567475216919199483376363835235927
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#8 by Seiichi Manyama at Sun Feb 26 02:13:46 EST 2023
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a(n) = Sum_{k=0..n} (4^k- - 1)^(n-k) * binomial(n,k).
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#7 by Seiichi Manyama at Sun Feb 26 02:12:34 EST 2023
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G.f.: Sum_{k>=0} x^k/(1 - (4^k - 1)*x)^(k+1).
a(n) = Sum_{k=0..n} (4^k-1)^(n-k) * binomial(n,k).
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#6 by Seiichi Manyama at Sun Feb 26 02:11:14 EST 2023
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| PROG
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(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1+sum(k=1, N, exp((4^k-1)*x)*x^k/k!)))
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(4^k-1)*x)^(k+1)))
(PARI) a(n) = sum(k=0, n, (4^k-1)^(n-k)*binomial(n, k));
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#5 by Seiichi Manyama at Sun Feb 26 02:02:05 EST 2023
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#4 by Seiichi Manyama at Sun Feb 26 02:00:42 EST 2023
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