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%I #3 Mar 30 2012 18:36:59
%S 1,2,9,52,425,4236,49294,655096,9731313,159114880,2832245911,
%T 54400757016,1119436524947,24532373640334,569732648555295,
%U 13962373137304496,359767723241891425,9715902692094061488
%N a(n) = [x^n] (1 + x*(1+x)^n )^(n+1).
%C a(n) is divisible by (n+1): a(n)/(n+1) = A121679(n).
%F a(n) = Sum_{k=0..n+1} C(n+1,k) * C(n*k,n-k).
%e At n=5, a(5) = [x^5] (1 + x*(1+x)^5)^6 = 4236, since
%e (1+x*(1+x)^5)^6 = 1 + 6*x + 45*x^2 + 230*x^3 + 1050*x^4 + 4236*x^5 +...
%o (PARI) a(n)=sum(k=0,n+1,binomial(n+1,k)*binomial(n*k,n-k))
%Y Cf. A121679; variants: A121673-A121676, A121680.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Aug 15 2006
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