A104510 G.f.: Product_{i>=1} (1 - 2*(-x)^i)/(1 - (-x)^i)^2.

0, -1, 2, -4, 4, -7, 4, -5, 0, 5, -18, 23, -46, 65, -82, 108, -132, 152, -164, 168, -144, 132, -48, -39, 212, -365, 658, -947, 1382, -1800, 2394, -2947, 3644, -4289, 5102, -5687, 6392, -6820, 7112, -7139, 6776, -5836, 4338, -2036, -1342, 5585, -11392, 18513, -27456, 37876, -51072, 65488, -82982, 101898

Offset: 1

Author

Vladeta Jovovic, Apr 19 2005

Keywords

• easy
• sign

Crossrefs

Cf. A000712, A077285.

Cf. A104575.

Programs

Maple

gf:=product((1-2*(-x)^i)/(1-(-x)^i)^2, i=1..100): s:=series(gf, x, 100): for n from 1 to 99 do printf(`%d,`,coeff(s, x, n)) od: # James Sellers, Apr 22 2005

Formula

a(n) = Sum (k(1)-1)*(k(2)-1)*...*(k(n)-1), where the sum is taken over all (k(1), k(2), ..., k(n)) such that k(1) + 2*k(2) + ... + n*k(n) = n, k(i) >= 0, i=1..n.

G.f.: Product_{i>=1} (1 - (-x)^i)^A052823(i). - James Sellers, Apr 22 2005

Extensions

More terms from James Sellers, Apr 22 2005