A367375 Expansion of the e.g.f. (exp(x) / (5 - 4*exp(x)))^(3/5).

1, 3, 21, 243, 3909, 80451, 2016885, 59610771, 2029183653, 78173046243, 3362038875093, 159665003673651, 8298290454862341, 468484406336978307, 28548397948780827957, 1867633303272817927635, 130551162799758211802469, 9710901131124428156535075

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+3)) * Stirling2(n,k).

a(0) = 1; a(n) = Sum_{k=1..n} (-1)^k * (2*k/n - 5) * binomial(n,k) * a(n-k).

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

Crossrefs

Cf. A136729, A201365, A367374, A367376.

Cf. A365569.

Sequence in context: A334262 A375900 A234855 * A058562 A145083 A234303

Adjacent sequences: A367372 A367373 A367374 * A367376 A367377 A367378

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2023

Status

approved