A383234 - OEIS

%I #7 Apr 20 2025 08:40:53

%S 0,1,13,218,4646,121080,3741144,133863792,5447294352,248518603584,

%T 12566268267840,697632464382336,42189230206182528,2760816706845539328,

%U 194381535085933095936,14652311175996819978240,1177370323796943823325184,100466288729505689717809152

%N Expansion of e.g.f. f(x)^4 * log(f(x)), where f(x) = 1/(1 - 5*x)^(1/5).

%F a(n) = Sum_{k=1..n} k * 4^(k-1) * 5^(n-k) * |Stirling1(n,k)|.

%F a(n) = 5^(n-1) * n! * Sum_{k=0..n-1} (-1)^k * binomial(-4/5,k)/(n-k).

%F a(n) = (10*n-7) * a(n-1) - (5*n-6)^2 * a(n-2) for n > 1.

%o (PARI) a(n) = sum(k=1, n, k*4^(k-1)*5^(n-k)*abs(stirling(n, k, 1)));

%Y Cf. A383231, A383232, A383233.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Apr 20 2025