Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #13 Sep 06 2024 06:24:52
%S 1,3,18,156,1758,24342,399480,7577700,163090500,3926104860,
%T 104520733560,3048811591680,96695722690200,3312942954681240,
%U 121938065727180480,4798400761979259120,201030443703421854480,8933622147642363338160,419725992843354254228640
%N Expansion of e.g.f. 1 / (1 + 2 * log(1 - x))^(3/2).
%F a(n) = Sum_{k=0..n} A001147(k+1) * |Stirling1(n,k)|.
%F a(n) ~ n^(n+1) / (exp(n/2) * (exp(1/2) - 1)^(n + 3/2)). - _Vaclav Kotesovec_, Sep 06 2024
%t nmax=18; CoefficientList[Series[1 / (1 + 2 * Log[1 - x])^(3/2),{x,0,nmax}],x]*Range[0,nmax]! (* _Stefano Spezia_, Sep 03 2024 *)
%o (PARI) a001147(n) = prod(k=0, n-1, 2*k+1);
%o a(n) = sum(k=0, n, a001147(k+1)*abs(stirling(n, k, 1)));
%Y Cf. A052801, A375946.
%Y Cf. A088500, A367474, A367475, A375953.
%Y Cf. A001147.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Sep 03 2024