A378091 - OEIS

%I #8 Nov 16 2024 10:21:43

%S 1,5,33,280,3009,40456,670351,13428794,318341841,8747362540,

%T 273595272231,9595433139238,372786185735497,15885841209363152,

%U 736549352642825247,36906793949098033906,1987212351128733260577,114415986259681057007956,7014281833059332148174007

%N E.g.f. satisfies A(x) = exp(x * (1-x)^3 * A(x)) / (1-x)^4.

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

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

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

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

%Y Cf. A323772, A352410, A378090.

%K nonn,new

%O 0,2

%A _Seiichi Manyama_, Nov 16 2024