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 A142962 Scaled convolution of (n^3)*A000984(n) with A000984(n). A000984(n) = binomial(2*n,n) (central binomial coefficients). 2

%I

%S 4,26,81,184,350,594,931,1376,1944,2650,3509,4536,5746,7154,8775,

%T 10624,12716,15066,17689,20600,23814,27346,31211,35424,40000,44954,

%U 50301,56056,62234,68850,75919,83456,91476,99994,109025,118584,128686,139346,150579

%N Scaled convolution of (n^3)*A000984(n) with A000984(n). A000984(n) = binomial(2*n,n) (central binomial coefficients).

%C S(3,n):= sum(p^3*binomial(2*p,p)*binomial(2*(n-p),n-p),p=0..n). a(n) = 2^3*S(3,n)/4^n, n>=1. O.g.f. for S(3,n) is G(k=3,x). See triangle A142963 for the general G(k,x) formula.

%C The author was led to compute such sums by a question asked by M. Greiter, Jun 27 2008.

%H Vincenzo Librandi, <a href="/A142962/b142962.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = n^2*(3+5*n)/2. a(0)=0.

%F a(n) = (2^3)*S(3,n)/4^n with the convolution S(3,n) defined above.

%F O.g.f.: 2*x*(1+10*x+4*x^2)/(1-4*x)^4 (see triangle A142963 for the general G(k,x) formula).

%Y A142961 triangle: row k=3: [3, 5], with the row polynomial 3+5*n.

%Y A049451 (scaled k=2 case).

%K nonn,easy

%O 1,1

%A _Wolfdieter Lang_ Sep 15 2008

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Last modified September 26 23:23 EDT 2021. Contains 347673 sequences. (Running on oeis4.)