A377553 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x*exp(x))^2 ).
1, 2, 14, 174, 3176, 77010, 2336892, 85316714, 3644408336, 178412603778, 9851421767060, 605826315779322, 41068369222584024, 3042849619010389058, 244657525386435161756, 21217387476442659806250, 1974219906922046702054432, 196191093901292764305110274, 20739322455031604846405387556
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, k^(n-k)*binomial(2*n+2, k)/(n-k)!)/(n+1);
Formula
E.g.f. satisfies A(x) = (1 + x * A(x) * exp(x*A(x)))^2.
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A364982.
a(n) = (n!/(n+1)) * Sum_{k=0..n} k^(n-k) * binomial(2*n+2,k)/(n-k)!.