A380257 Expansion of e.g.f. exp( (1/(1-3*x)^(2/3) - 1)/2 ).

1, 1, 6, 56, 706, 11186, 213156, 4742256, 120571676, 3447128796, 109427729096, 3818008773536, 145196289453656, 5976489668054296, 264685744187399536, 12548508890339297856, 634022724191046592016, 34007862777419093053456, 1929842567333195106456416

Offset

0,3

Links

Table of n, a(n) for n=0..18.

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/(1-3*x)^(2/3)-1)/2)))

Crossrefs

Cf. A049376, A375173, A380258.

Cf. A004211, A380214.

Sequence in context: A290788 A215507 A112699 * A093197 A303921 A052317

Adjacent sequences: A380254 A380255 A380256 * A380258 A380259 A380260

Keyword

nonn,new

Author

Seiichi Manyama, Jan 18 2025

Status

approved