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A332257 E.g.f.: (1 - sinh(x)) / (1 - 2*sinh(x)). 2

%I #12 Jul 26 2021 08:28:33

%S 1,1,4,25,208,2161,26944,391945,6515968,121866721,2532496384,

%T 57890223865,1443611004928,38999338931281,1134616226381824,

%U 35367467110007785,1175946733416153088,41543231955279099841,1553948045857778827264,61355543097139813855705

%N E.g.f.: (1 - sinh(x)) / (1 - 2*sinh(x)).

%H Michael De Vlieger, <a href="/A332257/b332257.txt">Table of n, a(n) for n = 0..401</a>

%H Paul Kinlaw, Michael Morris, and Samanthak Thiagarajan, <a href="https://www.researchgate.net/publication/350886459_SUMS_RELATED_TO_THE_FIBONACCI_SEQUENCE">Sums related to the Fibonacci sequence</a>, Husson University (2021).

%F a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A006154(k) * a(n-k).

%F a(n) ~ n! / (2*sqrt(5) * log((1 + sqrt(5))/2)^(n+1)). - _Vaclav Kotesovec_, Feb 08 2020

%t nmax = 19; CoefficientList[Series[(1 - Sinh[x])/(1 - 2 Sinh[x]), {x, 0, nmax}], x] Range[0, nmax]!

%o (PARI) seq(n)={Vec(serlaplace((1 - sinh(x + O(x*x^n))) / (1 - 2*sinh(x + O(x*x^n)))))} \\ _Andrew Howroyd_, Feb 08 2020

%Y Cf. A000557, A000670, A002866, A006154, A050351, A331608.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Feb 08 2020

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Last modified March 29 10:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)