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A320083
Expansion of e.g.f. Sum_{k>=0} log(1 + k*x)^k.
14
1, 1, 7, 116, 3574, 177094, 12873962, 1290494904, 170592253320, 28753159552272, 6018433850602848, 1531605185388897552, 465706857941949607008, 166746568516127626614288, 69440517484503283491716400, 33278913978673363553703249408, 18185279212166784139689388753536, 11239676837467731657648932618952576
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..n} Stirling1(n,k)*k!*k^n.
a(n) ~ c * d^n * n^(2*n + 1/2), where d = 0.298212940253960977992575968955431001807757948758929... and c = 3.40415549717199390989204785905061856492539214306... - Vaclav Kotesovec, Oct 05 2018
MAPLE
1, seq(n!*coeff(series(add( log(1 + k*x)^k, k=1..100), x=0, 18), x, n), n=1..17); # Paolo P. Lava, Jan 09 2019
MATHEMATICA
nmax = 17; CoefficientList[Series[1 + Sum[Log[1 + k x]^k, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
Join[{1}, Table[Sum[StirlingS1[n, k] k! k^n, {k, n}], {n, 17}]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 05 2018
STATUS
approved