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A365602
Expansion of e.g.f. 1 / (1 - 5 * log(1 + x))^(3/5).
7
1, 3, 21, 246, 3990, 82800, 2092560, 62343600, 2139137760, 83064002160, 3600715721040, 172353630085920, 9028586395211040, 513740204261763840, 31553316959017737600, 2080500578006553619200, 146577866381052082876800, 10988979300484733769667200
OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (5*j+3)) * Stirling1(n,k).
a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * (5 - 2*k/n) * (k-1)! * binomial(n,k) * a(n-k).
MATHEMATICA
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 *)
PROG
(PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 5*j+3)*stirling(n, k, 1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 11 2023
STATUS
approved