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A189919 O.g.f.: Sum_{n>=0} n! * x^n / Product_{k=1..n} (1 - (2*k-1)*x). 2

%I #24 Nov 01 2014 16:31:55

%S 1,1,3,15,105,933,10023,126195,1821165,29625513,536223723,10687190775,

%T 232544252625,5484912970893,139387510991823,3796699051667355,

%U 110344769466766485,3408297041928101073,111490951250101642323,3850360096498676899935

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

%H Vaclav Kotesovec, <a href="/A189919/b189919.txt">Table of n, a(n) for n = 0..350</a>

%F a(n) ~ 2^(n+1) * n! / (3^(3/2) * (log(3))^(n+1)). - _Vaclav Kotesovec_, Nov 01 2014

%e G.f.: A(x) = 1 + x + 3*x^2 + 15*x^3 + 105*x^4 + 933*x^5 + 10023*x^6 +...

%e where

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

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

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jul 22 2011

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