A367640 G.f. A(x) satisfies A(x) = (1 + x)^2 + x*A(x)^3 / (1 + x)^2.
1, 3, 8, 36, 200, 1220, 7896, 53220, 369528, 2624772, 18981864, 139287588, 1034475624, 7761249476, 58735359032, 447827171556, 3436759851672, 26526255859716, 205782644595912, 1603655203428900, 12548225647402248, 98548826076070596, 776552629964300952
Offset: 0
Keywords
Programs
-
PARI
a(n) = sum(k=0, n, binomial(2*k+2, n-k)*binomial(3*k, k)/(2*k+1));
Formula
a(n) = Sum_{k=0..n} binomial(2*k+2,n-k) * binomial(3*k,k)/(2*k+1).
D-finite with recurrence 2*n*(14*n+71)*(2*n+1)*a(n) +3*(-150*n^3-209*n^2-379*n+228)*a(n-1) +9*(-30*n^3-981*n^2+4297*n-3624)*a(n-2) +27*(n-4)*(22*n^2-491*n+1151)*a(n-3) +81*(n-4)*(n-5)*(6*n-49)*a(n-4)=0. - R. J. Mathar, Dec 04 2023