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A249636 G.f.: Sum_{n>=0} x^n / Product_{k=n..2*n-1} (1 - k*x). 1

%I

%S 1,1,2,7,33,186,1213,8949,73300,657589,6396829,66936872,748528619,

%T 8896663389,111873459298,1482522176651,20633389026901,300705290677218,

%U 4576892504775417,72584518271451169,1196883163316172252,20482129284796798609,363138667441109774065,6659922487212111452776

%N G.f.: Sum_{n>=0} x^n / Product_{k=n..2*n-1} (1 - k*x).

%H Vaclav Kotesovec, <a href="/A249636/b249636.txt">Table of n, a(n) for n = 0..350</a>

%e G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 33*x^4 + 186*x^5 + 1213*x^6 +...

%e where

%e A(x) = 1 + x/(1-x) + x^2/((1-2*x)*(1-3*x)) + x^3/((1-3*x)*(1-4*x)*(1-5*x)) + x^4/((1-4*x)*(1-5*x)*(1-6*x)*(1-7*x)) + x^5/((1-5*x)*(1-6*x)*(1-7*x)*(1-8*x)*(1-9*x)) +...

%o (PARI) {a(n)=polcoeff(sum(m=0,n,x^m/prod(k=m,2*m-1,1-k*x +x*O(x^n))),n)}

%o for(n=0,30,print1(a(n),", "))

%K nonn

%O 0,3

%A _Paul D. Hanna_, Nov 02 2014

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Last modified May 17 12:55 EDT 2021. Contains 343971 sequences. (Running on oeis4.)