A355171 - OEIS

A355171

a(n) = Sum_{k=0..n} binomial(n, k + 1)*k!*(n + 1)!/(k + 2)!.

0, 1, 7, 50, 406, 3804, 41028, 506064, 7084656, 111690720, 1967421600, 38425449600, 825970435200, 19404363283200, 495012834489600, 13632039812966400, 403120633444300800, 12740557701389414400, 428546132879432601600, 15284163618598275072000, 576073025410937628672000

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

FORMULA

a(n) = n*(n + 1)!*hypergeom([1, 1, 1 - n], [2, 3], -1) / 2.

a(n) = Sum_{k=0..n} (-1)^(k+1)*k!*A066667(n, k + 1).

E.g.f.: log((1 - x) / (1 - 2*x)) / (1 - x)^2. - Mélika Tebni, Jun 23 2022

a(n) ~ 2^(n+2) * (n-1)!. - Vaclav Kotesovec, Feb 17 2024

MAPLE

a := n -> n*(n + 1)!*hypergeom([1, 1, 1 - n], [2, 3], -1) / 2;