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a(n) ~ 21 * sqrt(3) * exp(Pi*sqrt(2*n/3)) / (24200 * Pi^2). - Vaclav Kotesovec, May 29 2018
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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 *)
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G.f.: (x^10/(1-x^10)^2-x^11/(1-x^11)^2)/Product_{i>=1}(1-x^i).
Alois P. Heinz, <a href="/A222738/b222738.txt">Table of n, a(n) for n = 10..1000</a>
b:= proc(n, p) option remember; `if`(n=0, [1, 0], `if`(p<1, [0, 0],
add((l->`if`(m=10, l+[0, l[1]*p], l))(b(n-p*m, p-1)), m=0..n/p)))
end:
a:= n-> b(n, n)[2]:
seq(a(n), n=10..60);
allocated for Alois P. Heinz
Total sum of parts of multiplicity 10 in all partitions of n.
1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 14, 16, 23, 28, 40, 49, 67, 82, 110, 135, 180, 220, 286, 349, 448, 548, 694, 846, 1061, 1290, 1608, 1948, 2406, 2909, 3566, 4300, 5242, 6298, 7637, 9149, 11044, 13189, 15847, 18872, 22582, 26817, 31967, 37858, 44970, 53116, 62894
10,5
Column k=10 of A222730.
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nonn
Alois P. Heinz, Mar 03 2013
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