A322381 Denominator of the sum of inverse products of parts in all strict partitions of n.

1, 1, 2, 6, 12, 60, 120, 280, 168, 210, 1680, 2640, 332640, 4324320, 8648640, 43243200, 900900, 735134400, 3150576, 2618916300, 83805321600, 586637251200, 586637251200, 749592043200, 2248776129600, 642507465600, 13492656777600, 41644002400, 53970627110400

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1268

Andreas B. G. Blobel, An Asymptotic Form of the Generating Function Prod_{k=1,oo} (1+x^k/k), arXiv:1904.07808 [math.CO], 2019.

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1) +b(n-i, min(i-1, n-i))/i))
    end:
a:= n-> denom(b(n$2)):
seq(a(n), n=0..30);

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1] + b[n - i, Min[i - 1, n - i]]/i]];
a[n_] := Denominator[b[n, n]];
a /@ Range[0, 30] (* Jean-François Alcover, Feb 25 2020, after Alois P. Heinz *)

Crossrefs

See A322380 for more information.

Sequence in context: A283487 A126915 A328450 * A265125 A328549 A002201

Adjacent sequences: A322378 A322379 A322380 * A322382 A322383 A322384

Keyword

nonn,frac

Author

Alois P. Heinz, Dec 05 2018

Status

approved