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 A121674 a(n) = [x^n] (1 + x*(1+x)^n )^n. 3

%I #7 Apr 17 2018 22:28:45

%S 1,1,5,28,233,2376,28102,379016,5707025,94439440,1699067321,

%T 32951077193,684009742319,15110032165151,353485501643471,

%U 8721374385748256,226128389777924385,6142306518887606112,174311816444805024379

%N a(n) = [x^n] (1 + x*(1+x)^n )^n.

%H Paul D. Hanna, <a href="/A121674/b121674.txt">Table of n, a(n) for n = 0..300</a>

%F a(n) = Sum_{k=0..n} C(n,k) * C(n*k,n-k).

%e At n=4, a(4) = [x^4] (1 + x*(1+x)^4 )^4 = 233, since

%e (1 + x*(1+x)^4 )^4 = 1 + 4*x + 22*x^2 + 76*x^3 + 233*x^4 +...

%t Table[Sum[Binomial[n,k] * Binomial[n*k,n-k], {k,0,n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Jun 12 2015 *)

%o (PARI) a(n)=sum(k=0,n,binomial(n,k)*binomial(n*k,n-k))

%Y Cf. variants: A121673, A121675-A121680.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Aug 15 2006

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