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A271371 Total number of inversions in all partitions of n into distinct parts. 3
0, 0, 0, 1, 1, 2, 5, 6, 9, 13, 22, 26, 38, 48, 66, 89, 113, 142, 185, 230, 289, 368, 449, 554, 679, 831, 1003, 1224, 1474, 1767, 2117, 2528, 2996, 3568, 4206, 4967, 5855, 6862, 8027, 9391, 10943, 12724, 14785, 17124, 19807, 22898, 26376, 30345, 34893, 40013 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..8950 (terms 0..5000 from Alois P. Heinz)

Wikipedia, Inversion (discrete mathematics)

FORMULA

a(n) = Sum_{k>=1} A161680(k) * A008289(n,k).

EXAMPLE

a(3) = 1: 21.

a(4) = 1: 31.

a(5) = 2: 32, 41.

a(6) = 5: 42, 51, 321 (three inversions).

MAPLE

b:= proc(n, i, t) option remember; `if`(n>i*(i+1)/2, 0,

     `if`(n=0, [1, 0], b(n, i-1, t)+`if`(i>n, 0,

      (p-> p+[0, p[1]*t])(b(n-i, i-1, t+1)))))

    end:

a:= n-> b(n$2, 0)[2]:

seq(a(n), n=0..60);

MATHEMATICA

b[n_, i_, t_] := b[n, i, t] = If[n > i*(i+1)/2, 0, If[n == 0, {1, 0}, b[n, i-1, t] + If[i>n, 0, Function[p, p+{0, p[[1]]*t}][b[n-i, i-1, t+1]]]]]; a[n_] := b[n, n, 0][[2]]; Table[a[n], {n, 0, 60}] (* Jean-Fran├žois Alcover, Feb 05 2017, translated from Maple *)

CROSSREFS

Cf. A000009, A008289, A161680, A271370, A271372.

Sequence in context: A030488 A190678 A255737 * A193978 A224486 A163782

Adjacent sequences:  A271368 A271369 A271370 * A271372 A271373 A271374

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 05 2016

STATUS

approved

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Last modified March 7 23:55 EST 2021. Contains 341933 sequences. (Running on oeis4.)