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%I #12 Mar 17 2024 06:05:48
%S 1,4,60,1584,60460,3029040,188149822,13957194496,1204226253180,
%T 118497226636800,13098496404605964,1607024046808249344,
%U 216700840893719564902,31857524157092264001280,5071166437655033657264250,868987068436739105218560000,159492062728455524910446791332,31215865935497559008870102593536,6489956761227888786183691062551704,1428394947783425181327275654594560000
%N a(n) is the coefficient of y^(n-1) in Product_{k=0..n-2} (n + (2*n + k)*y + n*y^2), for n >= 1.
%C a(n) = A324958(n,n-1) for n >= 1.
%H Vaclav Kotesovec, <a href="/A324959/b324959.txt">Table of n, a(n) for n = 1..300</a>
%F a(n) ~ n! * c * 5^(5*n) / (2^(8*n) * n^2), where c = 1/(5*Pi*sqrt(10*log(5/4))) = 0.04261749831824651172873387091554100360007169830546206828545398795767677148... - _Vaclav Kotesovec_, Oct 30 2019, updated Mar 17 2024
%t Table[If[n==1, 1, Coefficient[Expand[Product[(n + (2*n+k)*y + n*y^2), {k, 0, n-2}]], y^(n-1)]], {n, 1, 20}] (* _Vaclav Kotesovec_, Oct 30 2019 *)
%o (PARI) {a(n) = polcoeff( prod(k=0, n-2, n + (2*n+k)*y + n*y^2 +y*O(y^n)), n-1, y)}
%o for(n=1, 25, print1(a(n), ", "))
%Y Cf. A324958.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Mar 20 2019
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