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Expansion of e.g.f. 1 / sqrt(1 - 2 * x * (exp(x) - 1)).
0

%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