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

0,3

Comments

Binomial transform of A037256.

Links

Table of n, a(n) for n=0..21.

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

Mathematica

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

Crossrefs

Cf. A001339, A037256, A088128.

Sequence in context: A186997 A367239 A062265 * A369109 A082030 A348802

Adjacent sequences: A088126 A088127 A088128 * A088130 A088131 A088132

Keyword

easy,nonn

Author

Paul Barry, Sep 19 2003

Status

approved