A380260 Expansion of e.g.f. exp( ((1+2*x)^(3/2) - 1)/3 ).

1, 1, 2, 3, 9, 6, 111, -573, 7638, -95751, 1450431, -24643134, 468589617, -9843336567, 226448287794, -5662061186949, 152892006728841, -4434211761771978, 137468475061977663, -4536657554920874181, 158788359466681092966, -5875324355407515077439, 229142457698060305226367

Offset

0,3

Links

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

Eric Weisstein's World of Mathematics, Bell Polynomial.

Formula

a(n) = Sum_{k=0..n} 2^(n-k) * Stirling1(n,k) * A004212(k) = Sum_{k=0..n} 3^k * 2^(n-k) * Stirling1(n,k) * Bell_k(1/3), where Bell_n(x) is n-th Bell polynomial.

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

Prog

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

Crossrefs

Cf. A049425, A380259.

Sequence in context: A288842 A108694 A267896 * A199858 A357053 A340442

Adjacent sequences: A380257 A380258 A380259 * A380261 A380262 A380263

Keyword

sign,new

Author

Seiichi Manyama, Jan 18 2025

Status

approved