|
%I #17 Nov 08 2021 04:27:46
%S 1,2,22,504,16966,752800,41492284,2734083968,209681631814,
%T 18348172005888,1804161160185748,196945525458761728,
%U 23633625832975567644,3092337510752711057408,438161926888980929318584
%N Central coefficients of a scaled Legendre triangle.
%C Central coefficients of triangle A110124.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LegendrePolynomial.html">Legendre Polynomial</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Legendre_polynomials">Legendre polynomials</a>.
%F a(n)=2^n*LegendreP(n, n); a(n)=sum{j=0..floor(n/2), (-1)^j*C(n, j)C(2n-2j, n)n^(n-2j).
%F a(n) ~ 2^(2*n) * n^(n - 1/2) / sqrt(Pi). - _Vaclav Kotesovec_, Nov 07 2021
%t Table[2^n LegendreP[n,n],{n,0,20}] (* _Harvey P. Dale_, Nov 28 2012 *)
%o (PARI) a(n)=pollegendre(n,n)<<n \\ _Charles R Greathouse IV_, Mar 19 2017
%Y Cf. A008556, A349077, A349113, A349114, A349115.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Jul 13 2005
|
