A380262 Expansion of e.g.f. exp( ((1+5*x)^(2/5) - 1)/2 ).

1, 1, -2, 16, -206, 3682, -84236, 2348704, -77241380, 2926735516, -125540336024, 6013069027648, -318093606114536, 18418565715581656, -1158626159228481488, 78679416565851286144, -5736477278907382585328, 446936684375920051751440, -37056888825921886749507872

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} 5^(n-k) * Stirling1(n,k) * A004211(k) = Sum_{k=0..n} 2^k * 5^(n-k) * Stirling1(n,k) * Bell_k(1/2), where Bell_n(x) is n-th Bell polynomial.

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

Prog

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

Crossrefs

Cf. A000085, A002119, A380261.

Sequence in context: A036081 A303673 A367425 * A360466 A161568 A138429

Adjacent sequences: A380259 A380260 A380261 * A380263 A380264 A380265

Keyword

sign,new

Author

Seiichi Manyama, Jan 18 2025

Status

approved