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A278464
Total number of parts of the second sort in all partitions of n into two sorts of parts.
2
0, 1, 5, 17, 53, 145, 385, 957, 2333, 5493, 12741, 28941, 65049, 144225, 317229, 691457, 1497901, 3224145, 6906969, 14726701, 31282421, 66211253, 139720445, 294007373, 617154865, 1292516577, 2701451621, 5635565761, 11736442005, 24403092657, 50666528209
OFFSET
0,3
COMMENTS
a(n) is odd for n > 0.
LINKS
William Dugan, Sam Glennon, Paul E. Gunnells, Einar Steingrimsson, Tiered trees, weights, and q-Eulerian numbers, arXiv:1702.02446 [math.CO], Feb 2017
FORMULA
a(n) = Sum_{k=0..n} k * A256193(n,k).
MAPLE
b:= proc(n, i) option remember; `if`(n=0, [1/2, 0], `if`(i<1, 0,
b(n, i-1) +`if`(i>n, 0, (p-> p+[0, p[1]])(2*b(n-i, i)))))
end:
a:= n-> b(n$2)[2]:
seq(a(n), n=0..35);
MATHEMATICA
b[n_, i_] := b[n, i] = Expand[If[n == 0, 1, If[i < 1, 0, Sum[b[n - i*j, i - 1]*Sum[x^t*Binomial[j, t], {t, 0, j}], {j, 0, n/i}]]]];
a[n_] := Function[p, Table[Coefficient[p, x, i], {i, 0, n}]][b[n, n]] . Range[0, n];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Nov 10 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 22 2016
STATUS
approved