A365602 - OEIS

%I #12 Sep 13 2023 02:12:40

%S 1,3,21,246,3990,82800,2092560,62343600,2139137760,83064002160,

%T 3600715721040,172353630085920,9028586395211040,513740204261763840,

%U 31553316959017737600,2080500578006553619200,146577866381052082876800,10988979300484733769667200

%N Expansion of e.g.f. 1 / (1 - 5 * log(1 + x))^(3/5).

%F a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (5*j+3)) * Stirling1(n,k).

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

%t a[n_] := Sum[Product[5*j + 3, {j, 0, k - 1}] * StirlingS1[n, k], {k, 0, n}]; Array[a, 18, 0] (* _Amiram Eldar_, Sep 13 2023 *)

%o (PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 5*j+3)*stirling(n, k, 1));

%Y Cf. A347022, A365601, A365603, A365604.

%Y Cf. A365586.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 11 2023