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A361535
Expansion of g.f. 1 / Product_{n>=1} ((1 - x^n)^6 * (1 - x^(2*n-1))^4).
4
1, 10, 61, 290, 1172, 4212, 13833, 42262, 121625, 332764, 871641, 2197936, 5359005, 12679730, 29200593, 65617892, 144189054, 310400110, 655669910, 1360910666, 2779007594, 5589070978, 11081585154, 21679798590, 41883282555, 79958881544, 150943109191, 281926365224
OFFSET
0,2
LINKS
FORMULA
a(n) ~ exp(4*Pi*sqrt(n/3)) / (2^(5/2) * 3^(7/4) * n^(9/4)). - Vaclav Kotesovec, Mar 19 2023
EXAMPLE
G.f.: A(x) = 1 + 10*x + 61*x^2 + 290*x^3 + 1172*x^4 + 4212*x^5 + 13833*x^6 + 42262*x^7 + 121625*x^8 + 332764*x^9 + 871641*x^10 + ...
A related series begins
A(x)^(1/2) = 1 + 5*x + 18*x^2 + 55*x^3 + 149*x^4 + 371*x^5 + 867*x^6 + 1923*x^7 + 4086*x^8 + 8374*x^9 + ... + A360191(n)*x^n + ...
MATHEMATICA
nmax = 30; CoefficientList[Series[Product[1/((1 - x^k)^6 * (1 - x^(2*k-1))^4), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 19 2023 *)
PROG
(PARI) {a(n) = polcoeff( 1/prod(m=1, n, (1 - x^m)^6 * (1 - x^(2*m-1))^4 + x*O(x^n)), n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 18 2023
STATUS
approved