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A320343
Expansion of e.g.f. 1/sqrt(1 - 2*log(1 + x)).
8
1, 1, 2, 8, 42, 294, 2472, 24828, 286164, 3751428, 54864408, 887989200, 15731200680, 303068103480, 6304498706880, 140890167340560, 3365469544248720, 85585469309951760, 2308349518803845280, 65819488298810181120, 1978202007765686904480, 62505106242073569018720, 2071320752120227622985600
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} Stirling1(n,k)*A001147(k).
a(n) ~ n^n / ((exp(1/2) - 1)^(n + 1/2) * exp(n - 1/4)). - Vaclav Kotesovec, Jan 29 2019
a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * (2 - k/n) * (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, Sep 11 2023
MAPLE
seq(n!*coeff(series(1/sqrt(1-2*log(1+x)), x=0, 23), x, n), n=0..22); # Paolo P. Lava, Jan 29 2019
MATHEMATICA
nmax = 22; CoefficientList[Series[1/Sqrt[1 - 2 Log[1 + x]], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] (2 k - 1)!!, {k, 0, n}], {n, 0, 22}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 22 2019
STATUS
approved