A367373 Expansion of the e.g.f. (exp(x) / (4 - 3*exp(x)))^(3/4).

1, 3, 18, 171, 2223, 36648, 731763, 17157591, 461975868, 14045606613, 475876343583, 17777773950786, 725954222357613, 32168297036885103, 1537272547959690378, 78808327981017731631, 4314090689274124348083, 251157836896565547250368

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} (4*j+3)) * Stirling2(n,k).

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

a(0) = 1; a(n) = 3*a(n-1) + 3*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, 4*j+3)*stirling(n, k, 2));

Crossrefs

Cf. A136728, A201354, A367372.

Sequence in context: A099716 A352649 A113130 * A289683 A193098 A322771

Adjacent sequences: A367370 A367371 A367372 * A367374 A367375 A367376

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2023

Status

approved