A375224 Expansion of e.g.f. exp( x^2/(1-x)^3 ) / (1-x)^2.

1, 2, 8, 54, 492, 5400, 68520, 987000, 15928080, 284588640, 5570994240, 118432147680, 2714315123520, 66662973336960, 1745585471710080, 48522632817859200, 1426443527673964800, 44200671544495065600, 1439417651948346470400, 49134301244829555955200

Offset: 0

Author

Seiichi Manyama, Aug 06 2024

Keywords

• nonn

Crossrefs

Cf. A375172, A375225.

Cf. A052921, A361626.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x^2/(1-x)^3)/(1-x)^2))

PARI

a(n) = n!*sum(k=0, n\2, binomial(n+1+k, n-2*k)/k!);

Formula

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