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A110129
Central coefficients of a scaled Legendre triangle.
6
1, 2, 22, 504, 16966, 752800, 41492284, 2734083968, 209681631814, 18348172005888, 1804161160185748, 196945525458761728, 23633625832975567644, 3092337510752711057408, 438161926888980929318584
OFFSET
0,2
COMMENTS
Central coefficients of triangle A110124.
LINKS
Eric Weisstein's World of Mathematics, Legendre Polynomial.
FORMULA
a(n) = 2^n*LegendreP(n, n).
a(n) = Sum_{j=0..floor(n/2)} (-1)^j*C(n, j)*C(2*n-2*j, n)*n^(n-2*j).
a(n) ~ 2^(2*n) * n^(n - 1/2) / sqrt(Pi). - Vaclav Kotesovec, Nov 07 2021
MATHEMATICA
Table[2^n LegendreP[n, n], {n, 0, 20}] (* Harvey P. Dale, Nov 28 2012 *)
PROG
(PARI) a(n)=pollegendre(n, n)<<n \\ Charles R Greathouse IV, Mar 19 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 13 2005
STATUS
approved