A111335 Let qf(a,q) = Product_{j>=0} (1 - a*q^j); g.f. is qf(q^3,q^4)/qf(q,q^4).

1, 1, 1, 0, 0, 1, 1, 0, -1, 0, 2, 1, -1, -1, 1, 2, -1, -2, 1, 3, 1, -3, -1, 3, 1, -3, -2, 4, 4, -3, -4, 3, 5, -3, -7, 2, 9, 0, -9, -1, 10, 3, -11, -5, 12, 8, -11, -10, 10, 12, -11, -15, 11, 19, -7, -21, 6, 24, -5, -28, 1, 31, 4, -33, -8, 36, 12, -38, -18, 40, 27, -40, -33, 40, 39, -40, -49, 38, 60, -34, -67, 30, 75, -25, -87, 18, 98

Offset: 0

Author

N. J. A. Sloane, Nov 09 2005

Keywords

• sign
• look

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A111330.

Programs

Maple

# Uses EulerTransform from A358369.
a := EulerTransform(BinaryRecurrenceSequence(0, -1)):
seq(a(n), n=0..86); # Peter Luschny, Nov 17 2022

PARI

{a(n)=if(n<0, 0, polcoeff( prod(k=0,n\2, (1-x^(2*k+1))^(-(-1)^k), 1+x*O(x^n)), n))} /* Michael Somos, Nov 11 2005 */

Sage

# uses[EulerTransform from A166861]
b = BinaryRecurrenceSequence(0, -1)
a = EulerTransform(b)
print([a(n) for n in range(87)]) # Peter Luschny, Nov 17 2022

Formula

Euler transform of period 4 sequence [1, 0, -1, 0, ...]. - Michael Somos, Nov 10 2005

G.f.: Product_{k>0} (1-x^(2k-1))^((-1)^k). - Michael Somos, Nov 11 2005

G.f.: exp( Sum_{k >= 1} 1/(k*(x^k + x^(-k))) ). - Peter Bala, Sep 28 2023