A088129 Expansion of e.g.f. sinh(x)/(1-x)^2.

0, 1, 4, 19, 104, 661, 4812, 39607, 364240, 3704617, 41310740, 501328411, 6578864184, 92843236669, 1402257345244, 22570640656831, 385718738160032, 6975222838783057, 133078088319220260, 2671441145266564387, 56287972249358876680, 1242089553461115778021

Offset: 0

Author

Paul Barry, Sep 19 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A037256.

Crossrefs

Cf. A001339, A037256, A088128.

Programs

Mathematica

nmax=21; CoefficientList[Series[Sinh[x]/(1-x)^2, {x,0,nmax}], x]Range[0,nmax]! (* Stefano Spezia, Jan 15 2024 *)

Formula

a(n) = A001339(n) - A088128(n).

a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n,2*k+1) * (n-2*k)!. - Ilya Gutkovskiy, Apr 10 2022