A218571 - OEIS

%I #13 Sep 11 2017 02:36:14

%S 1,1,3,3,7,8,14,18,28,35,52,65,90,113,152,188,246,302,387,471,591,714,

%T 884,1059,1292,1538,1857,2193,2621,3077,3646,4254,4999,5801,6772,7815,

%U 9062,10409,12002,13719,15733,17909,20438,23169,26318,29722,33623,37833

%N Number of partitions p of n such that max(p)-min(p) = 8.

%H Alois P. Heinz, <a href="/A218571/b218571.txt">Table of n, a(n) for n = 10..1000</a>

%H G. E. Andrews, M. Beck and N. Robbins, <a href="https://arxiv.org/abs/1406.3374">Partitions with fixed differences between largest and smallest parts</a>, arXiv:1406.3374 [math.NT], 2014.

%F G.f.: Sum_{k>0} x^(2*k+8)/Product_{j=0..8} (1-x^(k+j)).

%F a(n) = A097364(n,8) = A116685(n,8) = A194621(n,8) - A194621(n,7) = A218510(n) - A218509(n).

%t terms = 48; offset = 10; max = terms + offset; s[k0_ /; k0 > 0] := Sum[x^(2*k + k0)/Product[ (1 - x^(k + j)), {j, 0, k0}], {k, 1, Ceiling[max/2]}] + O[x]^max // CoefficientList[#, x] &; Drop[s[8], offset] (* _Jean-François Alcover_, Sep 11 2017, after _Alois P. Heinz_ *)

%K nonn

%O 10,3

%A _Alois P. Heinz_, Nov 02 2012