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

Offset: 4

Author

Wolfdieter Lang, Jan 23 2004

Keywords

• nonn
• easy

Crossrefs

Cf. A091035 (fifth column of A090438).

Programs

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

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.:(sum(((-1)^(p+1))*binomial(7, p)*hypergeom([(p-1)/2, p/2], [], 4*x), p=2..7) + 6)/(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