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
KEYWORD
sign
AUTHOR
Paul D. Hanna, Oct 22 2017
STATUS
approved