A245157 G.f.: Sum_{n>=0} x^n/((1+x)^(2*n+1)*(1 - (2*n+1)*x)).

1, 1, 2, 7, 25, 108, 525, 2841, 16926, 109795, 768721, 5769848, 46170841, 392042257, 3517885530, 33240220095, 329703176361, 3423448119588, 37121182883557, 419414109036649, 4927952017449398, 60105139223521051, 759744837538329121, 9937680363610804080, 134328047043765078705

Offset: 0

Author

Paul D. Hanna, Jul 15 2014

Keywords

• nonn

Comments

Inspired by Peter Bala's formula in A229046.

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 25*x^4 + 108*x^5 + 525*x^6 +...
where
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)) +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A229046, A245156.

Programs

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)}
for(n=0, 30, print1(a(n), ", "))