A091036 Sixth column (k=7) of array A090438 ((4,2)-Stirling2) divided by 48 = 4!*2.

1, 840, 498960, 285405120, 173145772800, 115598414131200, 86165279456256000, 72034173625430016000, 67538393730337001472000, 70856069211827240140800000, 82901600977837870964736000000, 107758974298702617571000320000000, 155000508631253845114126860288000000

Offset

4,2

Links

Table of n, a(n) for n=4..16.

Formula

a(n) = A090438(n, 7)/48, n >= 4.

a(n) = binomial(2*n-2, 5)*(2*n)!/(7!*4!*2) = A053132(n+1)*(2*n)!/(7!*4!), n >= 4.

E.g.f.: (6 + Sum_{p=2..7} (-1)^(p+1)*binomial(7, p)*hypergeom([(p-1)/2, p/2], [], 4*x))/(7!*48) (cf. A090438).

D-finite with recurrence (2*n-7)*(n-4)*a(n) - 2*n*(n-1)*(2*n-1)*(2*n-3)*a(n-1) = 0. - R. J. Mathar, Jul 27 2022

a(n) ~ sqrt(Pi) * (2/e)^(2*n) * n^(2*n+11/2) / 453600. - Amiram Eldar, Nov 04 2025

Maple

A091036 := proc(n)
    binomial(2*n-2, 5)*(2*n)!/7!/4!/2 ;
end proc:
seq(A091036(n), n=4..40) ; # R. J. Mathar, Jul 27 2022

Mathematica

a[n_] := Binomial[2*n-2, 5] * (2*n)! / 241920; Array[a, 14, 4] (* Amiram Eldar, Nov 04 2025 *)

Crossrefs

Cf. A053132, A091035 (fifth column of A090438).

Sequence in context: A107516 A091035 A181203 * A091038 A121498 A331650

Adjacent sequences: A091033 A091034 A091035 * A091037 A091038 A091039

Keyword

nonn,easy

Author

Wolfdieter Lang, Jan 23 2004

Extensions

More terms from Amiram Eldar, Nov 04 2025

Status

approved