A380258 Expansion of e.g.f. exp( (1/(1-5*x)^(2/5) - 1)/2 ).

1, 1, 8, 106, 1954, 46082, 1323064, 44750644, 1741897340, 76672512316, 3764746706176, 203976645319448, 12086590557877144, 777464693554778776, 53948773488864143072, 4016672567726156437744, 319379204127841984947472, 27010128651142535536409360, 2420802590890201251989984128

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

Crossrefs

Cf. A049376, A375173, A380257.

Cf. A004211, A025168.

Sequence in context: A129278 A369512 A112701 * A099695 A236953 A345474

Adjacent sequences: A380255 A380256 A380257 * A380259 A380260 A380261

Keyword

nonn,new

Author

Seiichi Manyama, Jan 18 2025

Status

approved