A293132 - OEIS

A293132

G.f.: 2*q * Product_{n>=1} (1 + q^(2*n))/((1 + q^n)*(1 + q^(2*n-1))*(1 + q^(4*n))) in powers of q.

2, -4, 6, -12, 16, -24, 38, -52, 74, -104, 142, -192, 258, -340, 446, -584, 756, -972, 1244, -1580, 1996, -2516, 3148, -3924, 4878, -6032, 7434, -9136, 11182, -13644, 16608, -20148, 24378, -29428, 35422, -42540, 50978, -60940, 72700, -86556, 102838, -121952, 144360, -170564, 201176, -236900, 278494, -326876, 383094, -448288, 523824, -611248, 712256, -828860, 963324, -1118160, 1296296, -1501028, 1736030, -2005540

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OFFSET

1,1

COMMENTS

G.f. of row 1 in rectangular array A292929.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..2000

FORMULA

a(n) ~ -(-1)^n * 7^(1/4) * exp(sqrt(7*n/3)*Pi/2) / (2^(3/2) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Oct 23 2017

EXAMPLE

G.f.: A(q) = 2*q - 4*q^2 + 6*q^3 - 12*q^4 + 16*q^5 - 24*q^6 + 38*q^7 - 52*q^8 + 74*q^9 - 104*q^10 + 142*q^11 - 192*q^12 + 258*q^13 - 340*q^14 +...

MATHEMATICA

nmax = 50; CoefficientList[Series[2*Product[1/((1 + x^(2*k-1))^2 * (1 + x^(4*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 23 2017 *)

PROG

(PARI) {a(n) = polcoeff( 2*q * prod(m=1, n, (1 + q^(2*m))/((1 + q^m)*(1 + q^(2*m-1))*(1 + q^(4*m)) +q*O(q^n))), n, q)}

for(n=1, 60, print1(a(n), ", "))

CROSSREFS

Cf. A292929, A294065, A294066, A294067.

Sequence in context: A171609 A099316 A007416 * A098895 A266543 A378314

Adjacent sequences: A293129 A293130 A293131 * A293133 A293134 A293135

KEYWORD

sign

AUTHOR

Paul D. Hanna, Oct 22 2017

STATUS

approved