%I A121676
%S A121676 1,2,6,32,250,2412,27524,360600,5296050,85805420,1515794467,28926900312,
%T A121676 591903009295,12907255696636,298428274844730,7284351640977920,
%U A121676 187013495992710210,5033669346061547724,141643700005223732471
%N A121676 a(n) = [x^n] (1 + x*(1+x)^(n-1) )^(n+1).
%C A121676 a(n) is divisible by (n+1): a(n)/(n+1) = A121677(n).
%F A121676 a(n) = Sum_{k=0..n+1} C(n+1,k) * C((n-1)*k,n-k).
%e A121676 At n=4, a(4) = [x^4] (1 + x*(1+x)^3 )^5 = 250, since
%e A121676 (1 + x*(1+x)^3 )^5 = 1 + 5*x + 25*x^2 + 85*x^3 + 250*x^4 +...
%o A121676 (PARI) a(n)=sum(k=0,n+1,binomial(n+1,k)*binomial((n-1)*k,n-k))
%Y A121676 Cf. A121677; variants: A121673-A121675, A121678-A121680.
%Y A121676 Sequence in context: A012318 A012521 A012324 this_sequence A133596 A088437 
               A005736
%Y A121676 Adjacent sequences: A121673 A121674 A121675 this_sequence A121677 A121678 
               A121679
%K A121676 nonn
%O A121676 0,2
%A A121676 Paul D. Hanna (pauldhanna(AT)juno.com), Aug 15 2006