A362080 - OEIS

%I #10 Apr 09 2023 02:05:21

%S 1,1,7,55,571,7026,98925,1562219,27214867,516646333,10589130223,

%T 232574622116,5440521381816,134859301929873,3527034780915985,

%U 96965997588549555,2793286163779275779,84076751617833902070,2637677096916448507104

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

%H Seiichi Manyama, <a href="/A362080/b362080.txt">Table of n, a(n) for n = 0..449</a>

%F a(n) = Sum_{k=0..n} (-1)^k * binomial(-n,k) * binomial(n*k,n-k) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(n*k,n-k).

%o (PARI) a(n) = sum(k=0, n, binomial(n+k-1, k)*binomial(n*k, n-k));

%Y Main diagonal of A362078.

%Y Main diagonal of A362079.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Apr 08 2023