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A222738
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Total sum of parts of multiplicity 10 in all partitions of n.
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2
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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
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OFFSET
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10,5
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LINKS
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FORMULA
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G.f.: (x^10/(1-x^10)^2-x^11/(1-x^11)^2)/Product_{i>=1}(1-x^i).
a(n) ~ 21 * sqrt(3) * exp(Pi*sqrt(2*n/3)) / (24200 * Pi^2). - Vaclav Kotesovec, May 29 2018
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MAPLE
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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);
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MATHEMATICA
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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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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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