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Expansion of e.g.f. (1 - x * log(1 - x))^2.
2

%I #11 Nov 04 2024 09:15:01

%S 1,0,4,6,40,180,948,5880,42208,344736,3158640,32091840,358107264,

%T 4353972480,57290002560,811116633600,12295029657600,198666240675840,

%U 3408788192947200,61898371424870400,1185883197069312000,23905764186329088000,505813884019270041600

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

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

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

%Y Cf. A377683, A377684.

%Y Cf. A377685.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Nov 04 2024