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A070780 a(n) = binomial((n+1)^2,n).

%I A070780 #26 Apr 04 2025 15:45:22
%S A070780 1,4,36,560,12650,376992,13983816,621216192,32164253550,1902231808400,
%T A070780 126524771308936,9349109217266832,759825846558448488,
%U A070780 67362990324409227840,6469590128756692755600,669128737063722082963200,74148585178960981066746390,8764445804610791475090220464,1100718583140907766992803808200
%N A070780 a(n) = binomial((n+1)^2,n).
%C A070780 Previous name was: Binomial(binomial(n+1,n)^2,n).
%H A070780 Edward Jiang, <a href="/A070780/b070780.txt">Table of n, a(n) for n = 0..100</a>
%F A070780 a(n) = b(n-1) where b(n) = Sum_{i=1..n} binomial(i*n,i-1)*binomial(n^2-i*n,n-i)/i, n>0. - _Vladimir Kruchinin_, Nov 01 2013
%p A070780 A070780:=n->binomial((n+1)^2,n): seq(A070780(n),n=0..20); # _Wesley Ivan Hurt_, Aug 05 2014
%t A070780 Table[Binomial[(n + 1)^2, n], {n, 0, 20}] (* _Wesley Ivan Hurt_, Aug 05 2014 *)
%o A070780 (Maxima)
%o A070780 b(n):=sum((binomial(i*n,i-1)*binomial(n^2-i*n,n-i))/i,i,1,n);
%o A070780 makelist(b(n),n,1,10); /* _Vladimir Kruchinin_, Nov 01 2013 */
%o A070780 (PARI) a(n) = binomial((n+1)^2,n); \\ _Joerg Arndt_, Nov 01 2013
%o A070780 (Magma) [Binomial((n+1)^2,n) : n in [0..20]]; // _Wesley Ivan Hurt_, Aug 05 2014
%K A070780 nonn
%O A070780 0,2
%A A070780 _Karol A. Penson_, May 06 2002
%E A070780 New name and more terms from _Joerg Arndt_, Nov 01 2013