A324959 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.

1, 4, 60, 1584, 60460, 3029040, 188149822, 13957194496, 1204226253180, 118497226636800, 13098496404605964, 1607024046808249344, 216700840893719564902, 31857524157092264001280, 5071166437655033657264250, 868987068436739105218560000, 159492062728455524910446791332, 31215865935497559008870102593536, 6489956761227888786183691062551704, 1428394947783425181327275654594560000

Offset

1,2

Comments

a(n) = A324958(n,n-1) for n >= 1.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..300

Formula

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

Mathematica

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 *)

Prog

(PARI) {a(n) = polcoeff( prod(k=0, n-2, n + (2*n+k)*y + n*y^2 +y*O(y^n)), n-1, y)}
for(n=1, 25, print1(a(n), ", "))

Crossrefs

Cf. A324958.

Sequence in context: A013483 A013484 A013485 * A098630 A336637 A330069

Adjacent sequences: A324956 A324957 A324958 * A324960 A324961 A324962

Keyword

nonn

Author

Paul D. Hanna, Mar 20 2019

Status

approved