A132464 Let df(n,k) = Product_{i=0..k-1} (n-i) be the descending factorial and let P(m,n) = df(n-1,m-1)^2*(2*n-m)/((m-1)!*m!). Sequence gives P(6,n).

0, 0, 0, 0, 0, 1, 48, 735, 6272, 37044, 169344, 640332, 2090880, 6073353, 16032016, 39078039, 89037312, 191456720, 391523328, 766192176, 1442244096, 2622518073, 4623197040, 7925786407, 13248326784, 21641442900, 34616067200, 54311107500, 83710972800

Offset: 1

Author

Ottavio D'Antona (dantona(AT)dico.unimi.it), Oct 31 2007

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).

Crossrefs

See A132458 for further information.

Programs

Maple

seq((n - 5)^2*(n - 4)^2*(n - 3)^2*(n - 2)^2*(n - 1)^2*(2*n - 6)/86400, n=1..50); # Robert Israel, Jul 16 2020

Formula

From Robert Israel, Jul 16 2020: (Start)

a(n) = (n - 5)^2*(n - 4)^2*(n - 3)^2*(n - 2)^2*(n - 1)^2*(2*n - 6)/86400.

G.f.: (1 + 36*x + 225*x^2 + 400*x^3 + 225*x^4 + 36*x^5 + x^6)*x^6/(1 - x)^12. (End)