A375993 Expansion of e.g.f. (4 - 3 * exp(x))^(5/3).

1, -5, 5, 35, 165, 1075, 10805, 152035, 2719365, 58547475, 1469512405, 42082036035, 1353220758565, 48264167285875, 1890433757030005, 80656857839376035, 3723074712045197765, 184851684577600696275, 9822823990059902723605, 556226222504163445932035

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (3*j-5)) * Stirling2(n,k).

a(n) ~ 5 * sqrt(Pi) * 2^(29/6) * n^(n - 13/6) / (9 * Gamma(1/3) * exp(n) * log(4/3)^(n - 5/3)). - Vaclav Kotesovec, Sep 06 2024

Prog

(PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 3*j-5)*stirling(n, k, 2));

Crossrefs

Cf. A032033, A346982, A365558, A375949, A375952, A375992.

Sequence in context: A160555 A067047 A374508 * A271054 A270569 A270290

Adjacent sequences: A375990 A375991 A375992 * A375994 A375995 A375996

Keyword

sign,easy

Author

Seiichi Manyama, Sep 05 2024

Status

approved