A160528 Coefficients in the expansion of C^4/B^5, in Watson's notation of page 118.
1, 5, 20, 65, 190, 506, 1265, 2986, 6745, 14645, 30767, 62745, 124706, 242110, 460337, 858673, 1574140, 2839862, 5048435, 8852562, 15327290, 26224173, 44372688, 74301095, 123200079, 202394897, 329596348, 532299955, 852914900, 1356426196, 2141819621
Offset: 0
Keywords
Examples
G.f. = 1 + 5*x + 20*x^2 + 65*x^3 + 190*x^4 + 506*x^5 + 1265*x^6 + ... G.f. = q^23 + 5*q^47 + 20*q^71 + 65*q^95 + 190*q^119 + 506*q^143 + 1265*q^167 + ...
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..1000
- G. N. Watson, Ramanujans Vermutung über Zerfällungsanzahlen, J. Reine Angew. Math. (Crelle), 179 (1938), 97-128.
Programs
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Mathematica
nmax = 50; CoefficientList[Series[Product[(1 - x^(7*k))^4 /(1 - x^k)^5, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *)
Formula
See Maple code in A160525 for formula.
G.f.: Product_{n>=1} (1 - x^(7*n))^4/(1 - x^n)^5. - Seiichi Manyama, Nov 06 2016
a(n) ~ exp(Pi*sqrt(62*n/21)) * sqrt(31) / (4*sqrt(3) * 7^(5/2) * n). - Vaclav Kotesovec, Nov 10 2017