Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #9 Nov 15 2023 08:04:10
%S 1,3,21,243,3909,80451,2016885,59610771,2029183653,78173046243,
%T 3362038875093,159665003673651,8298290454862341,468484406336978307,
%U 28548397948780827957,1867633303272817927635,130551162799758211802469,9710901131124428156535075
%N Expansion of the e.g.f. (exp(x) / (5 - 4*exp(x)))^(3/5).
%F a(n) = Sum_{k=0..n} (-1)^(n-k) * (Product_{j=0..k-1} (5*j+3)) * Stirling2(n,k).
%F a(0) = 1; a(n) = Sum_{k=1..n} (-1)^k * (2*k/n - 5) * binomial(n,k) * a(n-k).
%F a(0) = 1; a(n) = 3*a(n-1) + 4*Sum_{k=1..n-1} binomial(n-1,k) * a(n-k).
%o (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*prod(j=0, k-1, 5*j+3)*stirling(n, k, 2));
%Y Cf. A136729, A201365, A367374, A367376.
%Y Cf. A365569.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Nov 15 2023