A380210 Expansion of e.g.f. exp( (1+2*x)^(5/2) - 1 ).

1, 5, 40, 365, 3835, 44420, 559375, 7569875, 108989500, 1659791375, 26571465625, 445392932000, 7785570546625, 141513486039125, 2666916967144000, 52000124771091125, 1046623556362721875, 21712732294602537500, 463350533965622059375, 10162009318486049571875

Offset

0,2

Comments

a(36) is negative.

Links

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

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+2*x)^(5/2)-1)))

Crossrefs

Cf. A380209.

Sequence in context: A052788 A213104 A219560 * A349362 A359984 A271957

Adjacent sequences: A380207 A380208 A380209 * A380211 A380212 A380213

Keyword

changed,sign

Author

Seiichi Manyama, Jan 16 2025

Status

approved