A378043 - OEIS

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

%S 1,2,13,190,4045,116746,4251289,187255174,9684799961,575477786674,

%T 38638577549701,2893159369162030,239045577899472997,

%U 21604942464613062010,2120362938300115706513,224568728344893756230326,25529660577970226603535793,3100816199696659908092912866

%N E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x) * A(x)^2 ).

%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) * exp( -LambertW(-2*x*(1+x)^3)/2 ).

%F a(n) = n! * Sum_{k=0..n} (2*k+1)^(k-1) * binomial(3*k+1,n-k)/k!.

%o (PARI) a(n) = n!*sum(k=0, n, (2*k+1)^(k-1)*binomial(3*k+1, n-k)/k!);

%Y Cf. A378019, A378044.

%Y Cf. A377894, A378045.

%Y Cf. A377894.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 15 2024