%I #10 Nov 15 2024 09:04:53

%S 1,2,17,349,10661,444161,23447635,1500738989,112954047113,

%T 9777254959729,956963374613471,104510139881448797,

%U 12599380858829314093,1662018439019972570681,238128379446158082330779,36825779588890274967294061,6113887910300601007096973585,1084611999181162104894547358561

%N E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x) * A(x)^3 ).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.

%F E.g.f.: (1+x) * exp( -LambertW(-3*x*(1+x)^4)/3 ).

%F a(n) = n! * Sum_{k=0..n} (3*k+1)^(k-1) * binomial(4*k+1,n-k)/k!.

%o (PARI) a(n) = n!*sum(k=0, n, (3*k+1)^(k-1)*binomial(4*k+1, n-k)/k!);

%Y Cf. A378019, A378043.

%Y Cf. A377895.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 15 2024