A365601 Expansion of e.g.f. 1 / (1 - 5 * log(1 + x))^(2/5).
1, 2, 12, 130, 1990, 39500, 962540, 27807120, 928991280, 35233882320, 1495508048160, 70233555485520, 3615667144284720, 202470393271792800, 12252576455326384800, 796817209624497196800, 55418456683474326892800, 4104671046431448576787200
Offset: 0
Keywords
Programs
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Mathematica
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 *)
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PARI
a(n) = sum(k=0, n, prod(j=0, k-1, 5*j+2)*stirling(n, k, 1));
Formula
a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (5*j+2)) * Stirling1(n,k).
a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * (5 - 3*k/n) * (k-1)! * binomial(n,k) * a(n-k).