A377861 - OEIS

%I #9 Nov 10 2024 05:01:10

%S 1,2,15,206,4193,113904,3882511,159475280,7672503681,423360926720,

%T 26362968645071,1829066086810368,139929538526047585,

%U 11703312997355442176,1062423600515479191375,104042389901715413633024,10933256593926589800851969,1227201235266954603172331520

%N Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^3 * 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))^3.

%F a(n) = n! * Sum_{k=0..n} (-1)^k * (n+1)^(k-1) * binomial(4*n-k+2,n-k)/k!.

%o (PARI) a(n) = n!*sum(k=0, n, (-1)^k*(n+1)^(k-1)*binomial(4*n-k+2, n-k)/k!);

%Y Cf. A377859, A377860.

%Y Cf. A377833.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 09 2024