A294119 Expansion of e.g.f.: exp(2*((1+x)^2 - 1)).

1, 4, 20, 112, 688, 4544, 31936, 236800, 1841408, 14943232, 126063616, 1101983744, 9954734080, 92714156032, 888502796288, 8746003922944, 88294183469056, 912920984944640, 9655688415674368, 104353064578711552, 1151244577906098176, 12953223477921316864

Offset: 0

Author

Seiichi Manyama, Oct 23 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..655

Crossrefs

Column k=2 of A294118.

Programs

Maple

f:= rectoproc({a(n)=4*a(n-1)+4*(n-1)*a(n-2),a(0)=1,a(1)=4},a(n),remember):
map(f, [$0..30]); # Robert Israel, Jun 16 2020

Mathematica

nmax = 20; CoefficientList[Series[E^(2*((1+x)^2 - 1)), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 23 2017 *)

PARI

N=66; x='x+O('x^N); Vec(serlaplace(exp(2*((1+x)^2-1))))

Formula

E.g.f.: exp(2*((1+x)^2 - 1)).

a(n) ~ 2^(n - 1/2) * n^(n/2) * exp(-1 + 2*sqrt(n) - n/2). - Vaclav Kotesovec, Oct 23 2017

a(n) = 4*a(n-1)+4*(n-1)*a(n-2). - Robert Israel, Jun 16 2020