A367376 Expansion of the e.g.f. (exp(x) / (5 - 4*exp(x)))^(4/5).

1, 4, 32, 400, 6800, 146128, 3795728, 115616848, 4040024720, 159282704848, 6993908053520, 338443123424080, 17894609985867152, 1026351961130219728, 63466858180767590672, 4209071260503851502160, 298006515851074633361552, 22434758711582422326267856

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * (Product_{j=0..k-1} (5*j+4)) * Stirling2(n,k).

a(0) = 1; a(n) = Sum_{k=1..n} (-1)^k * (k/n - 5) * binomial(n,k) * a(n-k).

a(0) = 1; a(n) = 4*a(n-1) + 4*Sum_{k=1..n-1} binomial(n-1,k) * a(n-k).

Prog

(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*prod(j=0, k-1, 5*j+4)*stirling(n, k, 2));

Crossrefs

Cf. A136729, A201365, A367374, A367375.

Cf. A365570, A365587, A365603.

Sequence in context: A325574 A373027 A113131 * A195762 A127670 A317403

Adjacent sequences: A367373 A367374 A367375 * A367377 A367378 A367379

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2023

Status

approved