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

0,2

Links

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

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

Example

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

Prog

(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 */

Crossrefs

Sequence in context: A361046 A241242 A009088 * A352409 A187662 A113065

Adjacent sequences: A245063 A245064 A245065 * A245067 A245068 A245069

Keyword

nonn

Author

Reinhard Zumkeller, Jul 11 2014

Status

approved