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A222736 Total sum of parts of multiplicity 8 in all partitions of n.

%I A222736 #10 May 29 2018 09:19:18
%S A222736 1,0,1,1,2,2,4,4,9,10,14,18,27,32,46,57,80,99,134,163,219,270,350,433,
%T A222736 561,686,875,1074,1349,1652,2062,2509,3116,3783,4650,5633,6893,8305,
%U A222736 10108,12153,14709,17630,21243,25371,30452,36271,43335,51478,61311,72598
%N A222736 Total sum of parts of multiplicity 8 in all partitions of n.
%H A222736 Alois P. Heinz, <a href="/A222736/b222736.txt">Table of n, a(n) for n = 8..1000</a>
%F A222736 G.f.: (x^8/(1-x^8)^2-x^9/(1-x^9)^2)/Product_{i>=1}(1-x^i).
%F A222736 a(n) ~ 17 * sqrt(3) * exp(Pi*sqrt(2*n/3)) / (10368 * Pi^2). - _Vaclav Kotesovec_, May 29 2018
%p A222736 b:= proc(n, p) option remember; `if`(n=0, [1, 0], `if`(p<1, [0, 0],
%p A222736       add((l->`if`(m=8, l+[0, l[1]*p], l))(b(n-p*m, p-1)), m=0..n/p)))
%p A222736     end:
%p A222736 a:= n-> b(n, n)[2]:
%p A222736 seq(a(n), n=8..60);
%t A222736 b[n_, p_] := b[n, p] = If[n == 0 && p == 0, {1, 0}, If[p == 0, Array[0&, n+2], Sum[Function[l, ReplacePart[l, m+2 -> p*l[[1]] + l[[m+2]]]][Join[b[n-p*m, p-1], Array[0&, p*m]]], {m, 0, n/p}]]]; a[n_] := b[n, n][[10]]; Table[a[n], {n, 8, 60}] (* _Jean-François Alcover_, Jan 24 2014, after _Alois P. Heinz_ *)
%Y A222736 Column k=8 of A222730.
%K A222736 nonn
%O A222736 8,5
%A A222736 _Alois P. Heinz_, Mar 03 2013