A305745 Expansion of Product_{k>=1} ((1 - k*x^k) / (1 + k*x^k))^k.

1, -2, -6, -4, 22, 72, 84, -32, -474, -1310, -1728, 60, 6420, 18712, 31080, 24992, -34074, -186468, -430138, -650612, -496296, 687120, 3599652, 8413968, 13374148, 12772246, -3910080, -50592280, -136089520, -244815336, -309079848, -176916784, 391358838

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..6234

Formula

Convolution of A266964 and A266971.

Convolution inverse of A266942.

Maple

N:= 50: # for a(0) .. a(N)
f:= mul(((1-k*x^k)/(1+k*x^k))^k, k=1..N):
S:= series(f, x, N+1):
seq(coeff(S, x, i), i=0..N); # Robert Israel, Mar 01 2024

Prog

(PARI) N=99; x='x+O('x^N); Vec(prod(k=1, N, ((1-k*x^k)/(1+k*x^k))^k))

Crossrefs

Cf. A266942, A266964, A266971, A292317.

Sequence in context: A202962 A019088 A096085 * A285988 A218973 A366652

Adjacent sequences: A305742 A305743 A305744 * A305746 A305747 A305748

Keyword

sign

Author

Seiichi Manyama, Jun 09 2018

Status

approved