A377716 E.g.f. satisfies A(x) = (1 + (exp(x) - 1) * A(x))^2.
1, 2, 12, 116, 1584, 28172, 619872, 16289996, 498428544, 17417438252, 684759380832, 29925135793676, 1439467532867904, 75591768584407532, 4303733247493423392, 264082643528395550156, 17375242687235713361664, 1220318925238762558532012, 91128522664443184593699552
Offset: 0
Programs
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PARI
a(n) = 2*sum(k=0, n, (2*k+1)!/(k+2)!*stirling(n, k, 2));
Formula
E.g.f.: 4/(1 + sqrt(5 - 4*exp(x)))^2.
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A052895.
a(n) = 2 * Sum_{k=0..n} (2*k+1)!/(k+2)! * Stirling2(n,k).
a(n) ~ 2^(5/2) * sqrt(5) * n^(n-1) / (exp(n) * log(5/4)^(n - 1/2)). - Vaclav Kotesovec, Aug 27 2025