%I #10 Aug 25 2024 09:57:59
%S 1,0,2,3,40,185,2436,20797,307616,3869217,66259900,1091351261,
%T 21671302368,437191547377,9981020325836,236821065758565,
%U 6144729994822336,167019469703969345,4868403452056231164,148845363155530699789,4822574537456548631360
%N Expansion of e.g.f. 1 / sqrt(1 - 2 * x * (exp(x) - 1)).
%F a(n) = n! * Sum_{k=0..floor(n/2)} A001147(k) * Stirling2(n-k,k)/(n-k)!.
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1-2*x*(exp(x)-1))))
%o (PARI) a001147(n) = prod(k=0, n-1, 2*k+1);
%o a(n) = n!*sum(k=0, n, a001147(k)*stirling(n-k, k, 2)/(n-k)!);
%Y Cf. A305404, A367880, A375687.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 24 2024