A380666 - OEIS

%I #8 Jan 30 2025 03:52:37

%S 1,3,33,670,20193,812736,41056921,2499780144,178288822305,

%T 14584953692800,1346528845766481,138513476506770432,

%U 15711724851356153857,1948422564510092267520,262263690685637016402825,38082186820362623941236736,5933845220766237850177220289,987599486681637240983472930816

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

%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)/(1 - x*A(x))^2.

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

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

%Y Cf. A380665.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 30 2025