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A365588 Expansion of e.g.f. 1 / (1 + 5 * log(1-x)). 6
1, 5, 55, 910, 20080, 553870, 18333050, 707959800, 31244562600, 1551289408800, 85579293493200, 5193226343508000, 343790892166398000, 24655487205067386000, 1904221630155352038000, 157574022827034258192000, 13908505761692419540320000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = Sum_{k=0..n} 5^k * k! * |Stirling1(n,k)|.
a(0) = 1; a(n) = 5 * Sum_{k=1..n} (k-1)! * binomial(n,k) * a(n-k).
a(n) ~ sqrt(2*Pi) * n^(n + 1/2) / (5 * exp(4*n/5) * (exp(1/5) - 1)^(n+1)). - Vaclav Kotesovec, Nov 11 2023
MATHEMATICA
a[n_] := Sum[5^k * k! * Abs[StirlingS1[n, k]], {k, 0, n}]; Array[a, 17, 0] (* Amiram Eldar, Sep 13 2023 *)
PROG
(PARI) a(n) = sum(k=0, n, 5^k*k!*abs(stirling(n, k, 1)));
CROSSREFS
Column k=5 of A320079.
Cf. A094418.
Sequence in context: A145662 A362653 A094418 * A367164 A008543 A057130
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 10 2023
STATUS
approved

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Last modified July 13 17:55 EDT 2024. Contains 374285 sequences. (Running on oeis4.)