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%I #36 Sep 11 2023 09:05:41
%S 1,1,2,8,42,294,2472,24828,286164,3751428,54864408,887989200,
%T 15731200680,303068103480,6304498706880,140890167340560,
%U 3365469544248720,85585469309951760,2308349518803845280,65819488298810181120,1978202007765686904480,62505106242073569018720,2071320752120227622985600
%N Expansion of e.g.f. 1/sqrt(1 - 2*log(1 + x)).
%F a(n) = Sum_{k=0..n} Stirling1(n,k)*A001147(k).
%F a(n) ~ n^n / ((exp(1/2) - 1)^(n + 1/2) * exp(n - 1/4)). - _Vaclav Kotesovec_, Jan 29 2019
%F 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
%p 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
%t nmax = 22; CoefficientList[Series[1/Sqrt[1 - 2 Log[1 + x]], {x, 0, nmax}], x] Range[0, nmax]!
%t Table[Sum[StirlingS1[n, k] (2 k - 1)!!, {k, 0, n}], {n, 0, 22}]
%Y Cf. A001147, A006252, A048994, A088501, A305404, A346978.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jan 22 2019
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