A380209 Expansion of e.g.f. exp( (1+2*x)^(3/2) - 1 ).

1, 3, 12, 51, 243, 1188, 6399, 33561, 207468, 1013769, 9226629, 6480972, 997054353, -13211542341, 359483683932, -8602977403413, 235389825828531, -6809489816432796, 211363316786680047, -6976456643635495839, 244258757298601120476, -9039628059778792352367, 352612224537284537865477

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * Stirling1(n,k) * Bell(k).

a(n) = (1/e) * 2^n * n! * Sum_{k>=0} binomial(3*k/2,n)/k!.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((1+2*x)^(3/2)-1)))

Crossrefs

Cf. A380210.

Sequence in context: A199875 A064036 A195255 * A241468 A224914 A227810

Adjacent sequences: A380189 A380190 A380208 * A380210 A380211 A380212

Keyword

sign,new

Author

Seiichi Manyama, Jan 16 2025

Status

approved