A252761 Total sum of n-th powers of parts in all partitions of n.

0, 1, 6, 39, 392, 4775, 73920, 1323441, 27530298, 644749920, 16877063274, 486936848068, 15373069624220, 526779275391863, 19477946814752586, 772859962684631760, 32758854443379036238, 1477205045259973740909, 70613293111837146235770, 3566735926987461858837256

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(n) = Sum_{j=1..n} A066633(n,j) * j^n.

a(n) ~ c * n^n, where c = 1/QPochhammer(exp(-1)) = 1.98244090741287370368568246556131201568288277843252568635840026086375046496... - Vaclav Kotesovec, May 28 2018, updated Jul 21 2018

Maple

b:= proc(n, p, k) option remember; `if`(n=0, [1, 0], `if`(p<1, [0, 0],
      add((l->`if`(m=0, l, l+[0, l[1]*p^k*m]))
          (b(n-p*m, p-1, k)), m=0..n/p)))
    end:
a:= n-> b(n$3)[2]:
seq(a(n), n=0..20);

Mathematica

b[n_, p_, k_] := b[n, p, k] = If[n == 0, {1, 0}, If[p < 1, {0, 0}, Sum[ Function[l, If[m == 0, l, l + {0, l[[1]]*p^k*m}]][b[n - p*m, p - 1, k]], {m, 0, n/p}]]]; a[n_] := b[n, n, n][[2]]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 07 2017, translated from Maple *)

Crossrefs

Main diagonal of A213191.

Cf. A066633.

Sequence in context: A124577 A352839 A006678 * A145709 A280006 A336291

Adjacent sequences: A252758 A252759 A252760 * A252762 A252763 A252764

Keyword

nonn

Author

Alois P. Heinz, Dec 21 2014

Status

approved