A380261 Expansion of e.g.f. exp( ((1+3*x)^(2/3) - 1)/2 ).

1, 1, 0, 2, -14, 146, -1944, 31620, -608068, 13502076, -340052704, 9579145016, -298455813160, 10191129869272, -378469678855904, 15187759126892976, -654936026064200944, 30203464484648818960, -1483333523694819075328, 77291514214052885054496

Offset

0,4

Links

Table of n, a(n) for n=0..19.

Eric Weisstein's World of Mathematics, Bell Polynomial.

Formula

a(n) = Sum_{k=0..n} 3^(n-k) * Stirling1(n,k) * A004211(k) = Sum_{k=0..n} 2^k * 3^(n-k) * Stirling1(n,k) * Bell_k(1/2), where Bell_n(x) is n-th Bell polynomial.

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

Prog

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

Crossrefs

Cf. A000085, A002119, A004211, A380262.

Sequence in context: A354286 A346432 A333592 * A087132 A380214 A036079

Adjacent sequences: A380258 A380259 A380260 * A380262 A380263 A380264

Keyword

sign

Author

Seiichi Manyama, Jan 18 2025

Status

approved