OFFSET
0,3
COMMENTS
Euler transform of the square pyramidal numbers (A000330).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Square Pyramidal Number
FORMULA
G.f.: Product_{k>=1} 1/(1 - x^k)^(k*(k+1)*(2*k+1)/6).
a(n) ~ exp(Zeta'(-1)/6 - Zeta(3)/(8*Pi^2) - Pi^16/(24883200000*Zeta(5)^3) + Pi^8*Zeta(3)/(1728000*Zeta(5)^2) - Zeta(3)^2/(720*Zeta(5)) + Zeta'(-3)/3 + (Pi^12/(43200000*2^(3/5)*Zeta(5)^(11/5)) - Pi^4*Zeta(3) / (3600*2^(3/5) * Zeta(5)^(6/5))) * n^(1/5) + (-Pi^8/(144000*2^(1/5)*Zeta(5)^(7/5)) + Zeta(3)/(12*2^(1/5)*Zeta(5)^(2/5))) * n^(2/5) + Pi^4/(180*2^(4/5)*Zeta(5)^(3/5)) * n^(3/5) + 5*Zeta(5)^(1/5)/2^(7/5) * n^(4/5)) * Zeta(5)^(23/225) / (2^(29/150) * sqrt(5*Pi) * n^(271/450)). - Vaclav Kotesovec, Dec 08 2016
MATHEMATICA
nmax=32; CoefficientList[Series[Product[1/(1 - x^k)^(k (k + 1) (2 k + 1)/6), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 08 2016
STATUS
approved