A218570 - OEIS

%I #13 Sep 11 2017 02:36:07

%S 1,1,3,3,7,8,14,18,28,34,51,63,86,108,144,175,229,278,351,425,529,630,

%T 775,919,1109,1309,1565,1827,2167,2518,2952,3414,3975,4563,5281,6036,

%U 6931,7889,9012,10200,11598,13078,14785,16613,18704,20925,23470,26174,29229

%N Number of partitions p of n such that max(p)-min(p) = 7.

%H Alois P. Heinz, <a href="/A218570/b218570.txt">Table of n, a(n) for n = 9..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+7)/Product_{j=0..7} (1-x^(k+j)).

%F a(n) = A097364(n,7) = A116685(n,7) = A194621(n,7) - A194621(n,6) = A218509(n) - A218508(n).

%t terms = 49; offset = 9; 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[7], offset] (* _Jean-François Alcover_, Sep 11 2017, after _Alois P. Heinz_ *)

%K nonn

%O 9,3

%A _Alois P. Heinz_, Nov 02 2012