A378044 E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x) * A(x)^3 ).
1, 2, 17, 349, 10661, 444161, 23447635, 1500738989, 112954047113, 9777254959729, 956963374613471, 104510139881448797, 12599380858829314093, 1662018439019972570681, 238128379446158082330779, 36825779588890274967294061, 6113887910300601007096973585, 1084611999181162104894547358561
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
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PARI
a(n) = n!*sum(k=0, n, (3*k+1)^(k-1)*binomial(4*k+1, n-k)/k!);
Formula
E.g.f.: (1+x) * exp( -LambertW(-3*x*(1+x)^4)/3 ).
a(n) = n! * Sum_{k=0..n} (3*k+1)^(k-1) * binomial(4*k+1,n-k)/k!.