OFFSET
0,2
COMMENTS
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 5001 terms from Vaclav Kotesovec)
FORMULA
a(n) ~ sqrt(c) * exp(sqrt(2*c*n)) / (8*Pi*n), where c = 2*Pi^2/3 + log(3)^2 + 2*polylog(2, -1/3) = 7.16861897522987077909937377164783326088308015803... .
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
(t-> b(t, min(t, i-1)))(n-i*j), j=1..n/i)*4 +b(n, i-1)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..44); # Alois P. Heinz, Aug 28 2019
MATHEMATICA
nmax = 40; CoefficientList[Series[Product[(1+3*x^k) / (1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]
PROG
(PARI) { my(n=40); Vec(prod(k=1, n, 4/(1-x^k) - 3 + O(x*x^n))) } \\ Andrew Howroyd, Dec 22 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jan 04 2016
STATUS
approved