A377390 - OEIS

%I #14 Oct 27 2024 09:25:16

%S 1,0,4,6,232,1380,46308,593880,20639456,434113344,16557009840,

%T 490894572960,20995513516800,801146038080960,38632110899469696,

%U 1791609186067646400,97167945389675212800,5275541489312858803200,319879838094553691744256,19820894989178283188198400

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

%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A371229.

%F a(n) = 2 * n! * (2*n+1)! * Sum_{k=0..floor(n/2)} |Stirling1(n-k,k)|/( (n-k)! * (2*n-k+2)! ).

%o (PARI) a(n) = 2*n!*(2*n+1)!*sum(k=0, n\2, abs(stirling(n-k, k, 1))/((n-k)!*(2*n-k+2)!));

%Y Cf. A371121, A377391.

%Y Cf. A371229, A377360.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 27 2024