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A320082 Expansion of e.g.f. Sum_{k>=0} log(1 + k*x)^k/k!. 4
1, 1, 3, 5, -60, -186, 13832, -98862, -8631360, 352796880, 4245955032, -1185349047048, 48595690153920, 3201334718188320, -607575977909763840, 26489851912606455504, 4482546578798646251520, -958939334596403708474880, 50300999315063602037775360, 14223928928980522264922223360, -3933112779003946549567400925696 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..n} Stirling1(n,k)*k^n.
MAPLE
1, seq(n!*coeff(series(add(log(1+k*x)^k/k!, k=1..100), x=0, 21), x, n), n=1..20); # Paolo P. Lava, Jan 09 2019
MATHEMATICA
nmax = 20; CoefficientList[Series[1 + Sum[Log[1 + k x]^k/k!, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
Join[{1}, Table[Sum[StirlingS1[n, k] k^n, {k, n}], {n, 20}]]
PROG
(PARI) a(n) = sum(k=0, n, stirling(n, k)*k^n); \\ Altug Alkan, Oct 05 2018
CROSSREFS
Sequence in context: A249011 A261533 A118477 * A273254 A222644 A181904
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Oct 05 2018
STATUS
approved

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Last modified May 25 11:12 EDT 2024. Contains 372788 sequences. (Running on oeis4.)