A380213 Expansion of e.g.f. exp( 1/(1-2*x)^(5/2) - 1 ).

1, 5, 60, 965, 19315, 459420, 12597775, 389902175, 13410470700, 506509866575, 20811096098725, 923085833362500, 43921261488000625, 2229827043134538125, 120239258292160027500, 6859351794101350278125, 412554191158956599261875, 26080572238227541202917500

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = Sum_{k=0..n} 5^k * 2^(n-k) * |Stirling1(n,k)| * Bell(k).

a(n) = (1/e) * (-2)^n * n! * Sum_{k>=0} binomial(-5*k/2,n)/k!.

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(1/(1-2*x)^(5/2)-1)))

Crossrefs

Cf. A049118, A380212.

Sequence in context: A093885 A192948 A234528 * A277300 A156125 A260776

Adjacent sequences: A380210 A380211 A380212 * A380214 A380215 A380216

Keyword

nonn

Author

Seiichi Manyama, Jan 16 2025

Status

approved