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Expansion of e.g.f. 1 / (1 - 5 * log(1 + x))^(2/5).
3

%I #11 Sep 13 2023 02:12:51

%S 1,2,12,130,1990,39500,962540,27807120,928991280,35233882320,

%T 1495508048160,70233555485520,3615667144284720,202470393271792800,

%U 12252576455326384800,796817209624497196800,55418456683474326892800,4104671046431448576787200

%N Expansion of e.g.f. 1 / (1 - 5 * log(1 + x))^(2/5).

%F a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (5*j+2)) * Stirling1(n,k).

%F a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * (5 - 3*k/n) * (k-1)! * binomial(n,k) * a(n-k).

%t a[n_] := Sum[Product[5*j + 2, {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+2)*stirling(n, k, 1));

%Y Cf. A347022, A365602, A365603, A365604.

%Y Cf. A365585.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 11 2023