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Combined weight, as defined at A244094, of the distinct-parts partitions of n.
3

%I #4 Jan 08 2014 05:36:23

%S 1,2,8,11,22,41,60,89,136,208,275,397,526,724,978,1279,1646,2172,2752,

%T 3518,4492,5620,7010,8742,10809,13280,16346,19937,24200,29373,35436,

%U 42548,51153,61039,72794,86632,102615,121268,143209,168458,197753,231833,270983

%N Combined weight, as defined at A244094, of the distinct-parts partitions of n.

%C These are the row sums of the array at A234923.

%t z = 45; p[n_] := p[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &]; q[n_] := q[n] = Length[p[n]]; v[n_] := v[n] = Table[n + 1 - i, {i, 1, n}]; w[n_, h_] := w[n, h] = Dot[p[n][[h]], v[Length[p[n][[h]]]]]; a[n_] := Sum[w[n, h], {h, 1, q[n]}]; Table[a[n], {n, 1, z}]

%Y Cf. A244093, A234097.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jan 01 2014