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A277060 a(n) = 1/2 * Sum_{k=0..n} (binomial(n,k) * binomial(n+k,k+1))^2 for n >= 0. 1

%I

%S 0,1,28,729,19376,529575,14835780,424231465,12338211520,363931754949,

%T 10862528888300,327501958094003,9959845931792784,305175084350065267,

%U 9412306255856822388,291982561878565118025,9104382992541189221120

%N a(n) = 1/2 * Sum_{k=0..n} (binomial(n,k) * binomial(n+k,k+1))^2 for n >= 0.

%H Seiichi Manyama, <a href="/A277060/b277060.txt">Table of n, a(n) for n = 0..656</a>

%F a(n) = n^2 * A074635(n)/2.

%o (PARI) a(n)=my(t=n); if(n<2, return(n)); sum(k=1,n, t*=(n-k+1)*(n+k)/k/(k+1); t^2, n^2)/2 \\ _Charles R Greathouse IV_, Nov 07 2016

%Y Cf. 1/2 * Sum_{k=0..n} (binomial(n,k) * binomial(n+k,k+1))^m: A050151 (m=1), this sequence (m=2).

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 07 2016

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Last modified July 5 06:34 EDT 2020. Contains 335459 sequences. (Running on oeis4.)