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%I #5 Jul 16 2014 09:21:53
%S 1,1,2,7,25,108,525,2841,16926,109795,768721,5769848,46170841,
%T 392042257,3517885530,33240220095,329703176361,3423448119588,
%U 37121182883557,419414109036649,4927952017449398,60105139223521051,759744837538329121,9937680363610804080,134328047043765078705
%N G.f.: Sum_{n>=0} x^n/((1+x)^(2*n+1)*(1 - (2*n+1)*x)).
%C Inspired by Peter Bala's formula in A229046.
%H Vaclav Kotesovec, <a href="/A245157/b245157.txt">Table of n, a(n) for n = 0..400</a>
%e G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 25*x^4 + 108*x^5 + 525*x^6 +...
%e where
%e A(x) = 1/((1+x)*(1-x)) + x/((1+x)^3*(1-3*x)) + x^2/((1+x)^5*(1-5*x))+ x^3/((1+x)^7*(1-7*x))+ x^4/((1+x)^9*(1-9*x)) + x^5/((1+x)^11*(1-11*x)) +...
%o (PARI) {a(n)=polcoeff( sum(m=0, n, x^m/((1+x)^(2*m+1)*(1 - (2*m+1)*x) +x*O(x^n))), n)}
%o for(n=0, 30, print1(a(n), ", "))
%Y Cf. A229046, A245156.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jul 15 2014
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