A132464 - OEIS

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

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OFFSET

1,7

LINKS

Table of n, a(n) for n=1..29.

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

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)

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

CROSSREFS

See A132458 for further information.

Sequence in context: A361188 A186162 A102279 * A145155 A105948 A350378

Adjacent sequences: A132461 A132462 A132463 * A132465 A132466 A132467

KEYWORD

nonn

AUTHOR

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

STATUS

approved