A377833 - OEIS

%I #8 Nov 09 2024 08:13:47

%S 1,4,51,1174,39833,1799136,101821723,6938396368,553482404721,

%T 50619262481920,5223014483031491,600332651141435136,

%U 76075005337204547209,10538051760153093320704,1584264031801742560408875,256912816791069951740348416,44703731640012047610981808097

%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} (n+1)^(k-1) * binomial(4*n-k+2,n-k)/k!.

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

%Y Cf. A377831, A377832.

%Y Cf. A377743, A377811.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 09 2024