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(7*n^3+4*n^2+4*n)*binomial(2*n,n)/30.
0

%I #7 May 15 2023 16:07:40

%S 0,1,16,158,1232,8358,51744,300300,1661088,8853702,45819488,231499268,

%T 1146562144,5584082140,26808586560,127118807640,596271746880,

%U 2770379517510,12763270285920,58358565060180,265032926077920,1196278125942900

%N (7*n^3+4*n^2+4*n)*binomial(2*n,n)/30.

%D Knuth, The Art of Computer Programming, Vol. 3, Section 5.2.1, Problem 15.

%t Table[(7n^3+4n^2+4n) Binomial[2n,n]/30,{n,0,40}] (* _Harvey P. Dale_, May 15 2023 *)

%K nonn

%O 0,3

%A _N. J. A. Sloane_.