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G.f.: Sum_{n>=0} x^n / Product_{k=1..2*n-1} (1 - k*x).
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%I #8 Nov 01 2014 04:34:33

%S 1,1,2,8,42,260,1860,15020,134336,1313696,13911528,158279872,

%T 1922455440,24794405328,338037825952,4853075024192,73123573392416,

%U 1152965052858560,18974557508679104,325181733420301504,5791431588096653824,106990656473333558528,2046805540661737323136

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

%C Compare to o.g.f. of Bell numbers: Sum_{n>=0} x^n / Product_{k=0..n} (1 - k*x).

%H Vaclav Kotesovec, <a href="/A229285/b229285.txt">Table of n, a(n) for n = 0..160</a>

%e G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 42*x^4 + 260*x^5 + 1860*x^6 +...

%e where

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

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

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

%Y Cf. A229286.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Sep 18 2013