A372246 E.g.f. A(x) satisfies A(x) = exp( x * A(x) * (1 + A(x)^(1/2)) ).
1, 2, 14, 182, 3528, 91572, 2988124, 117646664, 5429848160, 287596190960, 17197966810224, 1146212005029456, 84257333026857472, 6772618660901287040, 590968891266018673664, 55635634440230961625088, 5621016808791883758841344, 606656453852999167732922112
Offset: 0
Keywords
Programs
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PARI
a(n, r=1, t=1, u=1/2) = r*sum(k=0, n, (t*n+u*k+r)^(n-1)*binomial(n, k));
Formula
E.g.f.: A(x) = B(x)^2 where B(x) is the e.g.f. of A372251.
If e.g.f. satisfies A(x) = exp( r*x*A(x)^(t/r) * (1 + A(x)^(u/r)) ), then a(n) = r * Sum_{k=0..n} (t*n+u*k+r)^(n-1) * binomial(n,k).