A245156 G.f.: Sum_{n>=0} x^n/((1+x)^(2*n)*(1 - (2*n)*x)).

1, 1, 1, 4, 13, 51, 234, 1205, 6861, 42696, 287893, 2088343, 16195822, 133582909, 1166593665, 10746339324, 104072482781, 1056515903547, 11213782563474, 124152537651877, 1430804512710901, 17131971790847440, 212761333257548485, 2736258689605227615, 36389676240341831766

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 + x^2 + 4*x^3 + 13*x^4 + 51*x^5 + 234*x^6 +...
where
A(x) = 1 + x/((1+x)^2*(1-2*x)) + x^2/((1+x)^4*(1-4*x)) + x^3/((1+x)^6*(1-6*x))+ x^4/((1+x)^8*(1-8*x))+ x^5/((1+x)^10*(1-10*x)) + x^6/((1+x)^12*(1-12*x)) +...
		

Links

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

Crossrefs

Cf. A229046, A245157.

Programs

PARI

{a(n)=polcoeff( sum(m=0, n, x^m/((1+x)^(2*m)*(1 - 2*m*x) +x*O(x^n))), n)}
for(n=0, 30, print1(a(n), ", "))