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A222734 Total sum of parts of multiplicity 6 in all partitions of n.

%I A222734 #10 May 29 2018 09:19:34
%S A222734 1,0,1,1,2,2,6,6,9,12,18,22,36,43,62,77,107,133,186,229,306,384,499,
%T A222734 621,810,999,1277,1582,1997,2453,3088,3776,4698,5742,7088,8618,10592,
%U A222734 12824,15654,18910,22955,27615,33400,40028,48174,57593,69018,82231,98225
%N A222734 Total sum of parts of multiplicity 6 in all partitions of n.
%H A222734 Alois P. Heinz, <a href="/A222734/b222734.txt">Table of n, a(n) for n = 6..1000</a>
%F A222734 G.f.: (x^6/(1-x^6)^2-x^7/(1-x^7)^2)/Product_{i>=1}(1-x^i).
%F A222734 a(n) ~ 13 * sqrt(3) * exp(Pi*sqrt(2*n/3)) / (3528 * Pi^2). - _Vaclav Kotesovec_, May 29 2018
%p A222734 b:= proc(n, p) option remember; `if`(n=0, [1, 0], `if`(p<1, [0, 0],
%p A222734       add((l->`if`(m=6, l+[0, l[1]*p], l))(b(n-p*m, p-1)), m=0..n/p)))
%p A222734     end:
%p A222734 a:= n-> b(n, n)[2]:
%p A222734 seq(a(n), n=6..55);
%t A222734 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][[8]]; Table[a[n], {n, 6, 55}] (* _Jean-François Alcover_, Jan 24 2014, after _Alois P. Heinz_ *)
%Y A222734 Column k=6 of A222730.
%K A222734 nonn
%O A222734 6,5
%A A222734 _Alois P. Heinz_, Mar 03 2013