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%I #23 Mar 27 2017 21:32:09
%S 1,17,170,1275,7905,42619,206091,912475,3753600,14503040,53073898,
%T 185172670,619237835,1993524975,6200890505,18693654410,54763023032,
%U 156250892610,435071511875,1184288668525,3156320339542,8247548150893,21155326555195,53326448236250
%N Number of partitions of n into parts of 17 kinds.
%C a(n) is Euler transform of A010856. - _Alois P. Heinz_, Oct 17 2008
%H Alois P. Heinz, <a href="/A023015/b023015.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Pro#1mxtok">Index entries for expansions of Product_{k >= 1} (1-x^k)^m</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F a(0) = 1, a(n) = (17/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Mar 27 2017
%p 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
%t CoefficientList[Series[1/QPochhammer[x]^17, {x, 0, 30}], x] (* _Indranil Ghosh_, Mar 27 2017 *)
%o (PARI) Vec(1/eta(x)^17 + O(x^30)) \\ _Indranil Ghosh_, Mar 27 2017
%Y Cf. 17th column of A144064. - _Alois P. Heinz_, Oct 17 2008
%K nonn
%O 0,2
%A _David W. Wilson_