A377828 - OEIS

%I #11 Feb 16 2025 08:34:07

%S 1,4,21,193,2669,48711,1113325,30615019,984983193,36319515355,

%T 1510538562641,69968975169567,3572684914283941,199389519518767111,

%U 12075888110164192917,788850329621989132771,55289606764547108653361,4138807268239824817387443,329564746571982961088975257

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

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

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

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

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

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

%Y Cf. A377826, A377827.

%Y Cf. A377741, A377811.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 09 2024