A380513 Expansion of e.g.f. exp(x*G(x)) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
1, 1, 3, 31, 649, 20241, 831691, 42281023, 2558247441, 179401012129, 14301145772371, 1276863732880671, 126200478678828313, 13677209933635675441, 1612657716714084149019, 205505541279096688937791, 28144314031348292162103841, 4122178445898981809990411073, 642961375302043479923591655331
Offset: 0
Keywords
Programs
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PARI
a(n) = if(n==0, 1, n!*sum(k=0, n-1, binomial(n+3*k, k)/((n+3*k)*(n-k-1)!)));
Formula
a(n) = n! * Sum_{k=0..n-1} binomial(n+3*k,k)/((n+3*k) * (n-k-1)!) for n > 0.