A023015 Number of partitions of n into parts of 17 kinds.
1, 17, 170, 1275, 7905, 42619, 206091, 912475, 3753600, 14503040, 53073898, 185172670, 619237835, 1993524975, 6200890505, 18693654410, 54763023032, 156250892610, 435071511875, 1184288668525, 3156320339542, 8247548150893, 21155326555195, 53326448236250
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- Index entries for expansions of Product_{k >= 1} (1-x^k)^m
- N. J. A. Sloane, Transforms
Crossrefs
Cf. 17th column of A144064. - Alois P. Heinz, Oct 17 2008
Programs
-
Maple
with(numtheory): a:= proc(n) option remember; `if`(n=0, 1, add(add(d*17, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..40); # Alois P. Heinz, Oct 17 2008
-
Mathematica
CoefficientList[Series[1/QPochhammer[x]^17, {x, 0, 30}], x] (* Indranil Ghosh, Mar 27 2017 *) -
PARI
Vec(1/eta(x)^17 + O(x^30)) \\ Indranil Ghosh, Mar 27 2017
Formula
a(0) = 1, a(n) = (17/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017
a(n) ~ m^((m+1)/4) * exp(Pi*sqrt(2*m*n/3)) / (2^((3*m+5)/4) * 3^((m+1)/4) * n^((m+3)/4)) * (1 - ((9+Pi^2)*m^2+36*m+27) / (24*Pi*sqrt(6*m*n))), set m = 17. - Vaclav Kotesovec, Jun 28 2025
Comments