A377438 - OEIS

%I #39 Nov 05 2024 03:12:29

%S 1,0,4,6,136,660,13668,128520,2846240,41368320,1021615920,20260896480,

%T 564541372800,14159468157120,445236762450816,13446791658256320,

%U 474901138629918720,16708336544212992000,658279512232521209856,26360704394322974161920,1150065728368040063784960

%N E.g.f. satisfies A(x) = (1 - x * log(1 - x) * A(x))^2.

%F E.g.f.: 4/(1 + sqrt(1 + 4*x*log(1-x)))^2.

%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A371140.

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

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

%Y Cf. A052830, A377691.

%Y Cf. A371140.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 04 2024