A367375 - 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