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

1, 1, 4, 25, 208, 2161, 26944, 391945, 6515968, 121866721, 2532496384, 57890223865, 1443611004928, 38999338931281, 1134616226381824, 35367467110007785, 1175946733416153088, 41543231955279099841, 1553948045857778827264, 61355543097139813855705

Offset

0,3

Links

Michael De Vlieger, Table of n, a(n) for n = 0..401

Paul Kinlaw, Michael Morris, and Samanthak Thiagarajan, Sums related to the Fibonacci sequence, Husson University (2021).

Formula

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

a(n) ~ n! / (2*sqrt(5) * log((1 + sqrt(5))/2)^(n+1)). - Vaclav Kotesovec, Feb 08 2020

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A061714 A005411 A105628 * A203219 A064299 A261898

Adjacent sequences: A332254 A332255 A332256 * A332258 A332259 A332260

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 08 2020

Status

approved