A245066 Central terms of triangles A001497 and A001498.

1, 3, 45, 1260, 51975, 2837835, 192972780, 15713497800, 1490818103775, 161505294575625, 19671344879311125, 2660996470946814000, 395823225053338582500, 64214706279807005422500, 11283441246308945238525000, 2134827083801652439128930000

Offset: 0

Author

Reinhard Zumkeller, Jul 11 2014

Keywords

• nonn

Examples

			G.f. = 1 + 3*x + 45*x^2 + 1260*x^3 + 51975*x^4 + 2837835*x^5 + ...
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..250

Programs

Haskell

a245066 n = a001497 (2 * n) n

PARI

{a(n) = if( n<0, 0, (3*n)! / (2^n * n!^2))}; /* Michael Somos, Jul 11 2014 */

Formula

a(n) = A001497(2*n,n) = A001498(2*n,n).

O.g.f. A(x) satisfies 0 = 6*A(x) + (-2 + 54*x) * A'(x) + 27*x^2 * A''(x). - Michael Somos, Jul 11 2014

E.g.f. A(x) satisfies 0 = 6*A(x) + (-2 + 54*x) * A'(x) + (-2*x + 27*x^2) * A''(x). - Michael Somos, Jul 11 2014

a(n) = (3*n)! / (2^n * n!^2). - Michael Somos, Jul 11 2014

a(n) = (2*n-1)!! * [x^(2*n)] x^n/(1 - x)^(2*n+1). - Ilya Gutkovskiy, Nov 24 2017