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A278556
Expansion of Product_{n>=1} (1 - x^(5*n))^18/(1 - x^n)^19 in powers of x.
11
1, 19, 209, 1710, 11495, 66862, 347339, 1645875, 7221520, 29668595, 115116233, 424720338, 1498263563, 5076482415, 16583497160, 52399330389, 160586833362, 478482249548, 1388989067820, 3935549005725, 10901608510397, 29565343541110, 78604103339462
OFFSET
0,2
LINKS
FORMULA
G.f.: Product_{n>=1} (1 - x^(5*n))^18/(1 - x^n)^19.
A278559(n) = 5^2*63*A160460(n) + 5^5*52*A278555(n-1) + 5^7*63*a(n-2) + 5^10*6*A278557(n-3) + 5^12*A278558(n-4) for n >= 4.
a(n) ~ sqrt(77/15) * exp(Pi*sqrt(154*n/15)) / (7812500*n). - Vaclav Kotesovec, Nov 28 2016
MATHEMATICA
CoefficientList[ Series[ Product[(1 - x^(5n))^18/(1 - x^n)^19, {n, 22}], {x, 0, 22}], x] (* Robert G. Wilson v, Nov 24 2016 *)
CROSSREFS
Cf. Product_{n>=1} (1 - x^(5*n))^k/(1 - x^n)^(k + 1): A160461 (k=1), A160462 (k=2), A160463 (k=3), A160506 (k=4), A071734 (k=5), A160460 (k=6), A160521 (k=7), A278555 (k=12), this sequence (k=18), A278557 (k=24), A278558 (k=30).
Sequence in context: A180364 A125407 A289423 * A023017 A022647 A032613
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 23 2016
STATUS
approved