A367376 - OEIS

%I #10 Nov 15 2023 08:04:14

%S 1,4,32,400,6800,146128,3795728,115616848,4040024720,159282704848,

%T 6993908053520,338443123424080,17894609985867152,1026351961130219728,

%U 63466858180767590672,4209071260503851502160,298006515851074633361552,22434758711582422326267856

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

%F a(n) = Sum_{k=0..n} (-1)^(n-k) * (Product_{j=0..k-1} (5*j+4)) * Stirling2(n,k).

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

%F a(0) = 1; a(n) = 4*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+4)*stirling(n, k, 2));

%Y Cf. A136729, A201365, A367374, A367375.

%Y Cf. A365570, A365587, A365603.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 15 2023