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A132464
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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).
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1
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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
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1,7
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).
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FORMULA
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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)
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MAPLE
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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
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CROSSREFS
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See A132458 for further information.
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KEYWORD
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nonn
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AUTHOR
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Ottavio D'Antona (dantona(AT)dico.unimi.it), Oct 31 2007
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STATUS
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approved
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