The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A202617 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A202617

E.g.f. satisfies: A(x) = exp( x*(1 + A(x)^2)/2 ).
(history; published version)

#25 by Michel Marcus at Sun Sep 27 03:08:41 EDT 2020

STATUS

reviewed

approved

#24 by Joerg Arndt at Sun Sep 27 03:04:22 EDT 2020

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proposed

reviewed

#23 by Seiichi Manyama at Sun Sep 27 02:58:35 EDT 2020

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editing

proposed

#22 by Seiichi Manyama at Sun Sep 27 02:56:43 EDT 2020

LINKS

Seiichi Manyama, <a href="/A202617/b202617.txt">Table of n, a(n) for n = 0..372</a>

STATUS

approved

editing

#21 by Charles R Greathouse IV at Tue Jul 19 11:33:31 EDT 2016

STATUS

editing

approved

#20 by Charles R Greathouse IV at Tue Jul 19 11:33:04 EDT 2016

PROG

(PARI) {a(n)=local(A=1+x); for(i=0, n, A=exp(x*(1+A^2)/2 +x*O(x^n))); n!*polcoeff(A, n)}

(PARI) {a(n)=n!*polcoeff(exp(sum(k=1, n, k^(k-1)*cosh(k*x +x*O(x^n))*x^k/k!) +x*O(x^n)), n)} \\ _Paul D. Hanna_, Nov 20 2012

for(n=0, 25, print1(a(n), ", ")) \\ _Paul D. Hanna_, Nov 20 2012

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approved

editing

#19 by Bruno Berselli at Fri Jan 10 17:04:17 EST 2014

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proposed

approved

#18 by Vaclav Kotesovec at Fri Jan 10 15:54:29 EST 2014

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editing

proposed

#17 by Vaclav Kotesovec at Fri Jan 10 15:54:10 EST 2014

FORMULA

E.g.f.: sqrt(-LambertW(-x*exp(x))/x). - Vaclav Kotesovec, Jan 10 2014

#16 by Vaclav Kotesovec at Fri Jan 10 15:53:37 EST 2014

FORMULA

a(n) ~ sqrt(1+c) * n^(n-1) / (2 * exp(n) * c^(n+1/2)), where c = LambertW(exp(-1)) = 0.278464542761... (see A202357). - Vaclav Kotesovec, Jan 10 2014

CROSSREFS

Cf. A007889, A058014, A214225, A138860, A202357.