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A222738 Total sum of parts of multiplicity 10 in all partitions of n.

%I A222738 #10 May 29 2018 09:18:25
%S A222738 1,0,1,1,2,2,4,4,7,8,14,16,23,28,40,49,67,82,110,135,180,220,286,349,
%T A222738 448,548,694,846,1061,1290,1608,1948,2406,2909,3566,4300,5242,6298,
%U A222738 7637,9149,11044,13189,15847,18872,22582,26817,31967,37858,44970,53116,62894
%N A222738 Total sum of parts of multiplicity 10 in all partitions of n.
%H A222738 Alois P. Heinz, <a href="/A222738/b222738.txt">Table of n, a(n) for n = 10..1000</a>
%F A222738 G.f.: (x^10/(1-x^10)^2-x^11/(1-x^11)^2)/Product_{i>=1}(1-x^i).
%F A222738 a(n) ~ 21 * sqrt(3) * exp(Pi*sqrt(2*n/3)) / (24200 * Pi^2). - _Vaclav Kotesovec_, May 29 2018
%p A222738 b:= proc(n, p) option remember; `if`(n=0, [1, 0], `if`(p<1, [0, 0],
%p A222738       add((l->`if`(m=10, l+[0, l[1]*p], l))(b(n-p*m, p-1)), m=0..n/p)))
%p A222738     end:
%p A222738 a:= n-> b(n, n)[2]:
%p A222738 seq(a(n), n=10..60);
%t A222738 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][[12]]; Table[a[n], {n, 10, 60}] (* _Jean-François Alcover_, Jan 24 2014, after _Alois P. Heinz_ *)
%Y A222738 Column k=10 of A222730.
%K A222738 nonn
%O A222738 10,5
%A A222738 _Alois P. Heinz_, Mar 03 2013