A258342 Expansion of Product_{k>=1} (1+x^k)^(k*(k+1)*(k+2)).

1, 6, 39, 224, 1131, 5412, 24411, 105078, 435048, 1740312, 6755877, 25533330, 94205738, 340064322, 1203313782, 4180514846, 14279610417, 48013553310, 159086287869, 519912616614, 1677331973910, 5345927500226, 16843574682291, 52494817082952, 161923200857711

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Formula

a(n) ~ 3^(1/5) * Zeta(5)^(1/10) / (2^(91/120) * 5^(2/5) * sqrt(Pi) * n^(3/5)) * exp(-2401*Pi^16 / (1749600000000 * Zeta(5)^3) + 49*Pi^8 * Zeta(3) / (2700000 * Zeta(5)^2) - Zeta(3)^2 / (25*Zeta(5)) + (343*Pi^12/(405000000 * 2^(4/5) * 3^(2/5) * 5^(1/5) * Zeta(5)^(11/5)) - 7*Pi^4 * Zeta(3) / (750 * 2^(4/5) * 3^(2/5) * 5^(1/5) * Zeta(5)^(6/5))) * n^(1/5) + (-49*Pi^8 / (180000 * 2^(3/5) * 3^(4/5) * 5^(2/5) * Zeta(5)^(7/5)) + 3^(1/5) * Zeta(3) / (2^(3/5) * (5*Zeta(5))^(2/5))) * n^(2/5) + 7*Pi^4 / (180 * 2^(2/5) * 3^(1/5) * (5*Zeta(5))^(3/5)) * n^(3/5) + 5*3^(2/5) * (5*Zeta(5)/2)^(1/5)/4 * n^(4/5)), where Zeta(3) = A002117, Zeta(5) = A013663.

Mathematica

nmax=30; CoefficientList[Series[Product[(1+x^k)^(k*(k+1)*(k+2)), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A248882, A028377, A258341, A258343, A258344, A258345, A258346, A258350.

Sequence in context: A297579 A229600 A339205 * A037592 A037683 A145664

Adjacent sequences: A258339 A258340 A258341 * A258343 A258344 A258345

Keyword

nonn

Author

Vaclav Kotesovec, May 27 2015

Status

approved