A110129 Central coefficients of a scaled Legendre triangle.

1, 2, 22, 504, 16966, 752800, 41492284, 2734083968, 209681631814, 18348172005888, 1804161160185748, 196945525458761728, 23633625832975567644, 3092337510752711057408, 438161926888980929318584, 66838962347916069718425600, 10921339483491720513675526726, 1903085098399657078831752282112

Offset

0,2

Comments

Central coefficients of triangle A110124.

Links

Table of n, a(n) for n=0..17.

Eric Weisstein's World of Mathematics, Legendre Polynomial.

Wikipedia, Legendre polynomials.

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

Maple

a:= n-> LegendreP(n$2)*2^n:
seq(a(n), n=0..17);  # Alois P. Heinz, Nov 17 2024

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

Cf. A008556, A110124, A349077, A349113, A349114, A349115.

Sequence in context: A137076 A090730 A090313 * A328020 A246740 A248798

Adjacent sequences: A110126 A110127 A110128 * A110130 A110131 A110132

Keyword

easy,nonn,changed

Author

Paul Barry, Jul 13 2005

Status

approved