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A285199
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Product of n! and the n-th Legendre polynomial evaluated at 2.
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0
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1, 2, 11, 102, 1329, 22290, 457155, 11083590, 310107105, 9834291810, 348584413275, 13657116176550, 586048630115025, 27335806776328050, 1377091347432275475, 74513480022911679750, 4309990208248262162625, 265383902858519912717250, 17331286029912646125208875
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = P_n(2)*n!, where P_n is the n-th Legendre polynomial.
D-finite with recurrence: a(n+2) = (4n+6) a(n+1) - (n+1)^2 a(n). - Robert Israel, May 05 2017
a(n) ~ 3^(-1/4) * (2 + sqrt(3))^(n + 1/2) * n^n / exp(n). - Vaclav Kotesovec, May 06 2017
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MAPLE
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seq(orthopoly[P](n, 2)*n!, n=0..30); # Robert Israel, May 05 2017
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MATHEMATICA
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PROG
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(Python)
from sympy import legendre, factorial
def a(n): return legendre(n, 2)*factorial(n)
(PARI) a(n) = n!*pollegendre(n, 2); \\ Michel Marcus, May 06 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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