A377860 - OEIS

%I #9 Nov 10 2024 05:02:11

%S 1,1,5,44,577,10104,222133,5886880,182775969,6509571200,261665344261,

%T 11720054882304,578878362625825,31259890045425664,1832295378792935925,

%U 115862322601669627904,7861907382202262095297,569837358810005613281280,43939338917141224534941829

%N Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^2 * exp(x) ).

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

%F E.g.f. A(x) satisfies A(x) = exp(-x * A(x))/(1 - x*A(x))^2.

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

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

%Y Cf. A377859, A377861.

%Y Cf. A377832.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 09 2024