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A222733 Total sum of parts of multiplicity 5 in all partitions of n. 2
1, 0, 1, 1, 2, 4, 6, 6, 11, 14, 23, 29, 43, 52, 76, 100, 135, 174, 235, 294, 397, 500, 651, 821, 1060, 1324, 1692, 2107, 2658, 3297, 4139, 5089, 6339, 7778, 9604, 11746, 14425, 17533, 21427, 25960, 31548, 38080, 46070, 55375, 66718, 79957, 95906, 114555 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 5..1000

FORMULA

G.f.: (x^5/(1-x^5)^2-x^6/(1-x^6)^2)/Product_{i>=1}(1-x^i).

a(n) ~ 11 * sqrt(3) * exp(Pi*sqrt(2*n/3)) / (1800 * Pi^2). - Vaclav Kotesovec, May 29 2018

MAPLE

b:= proc(n, p) option remember; `if`(n=0, [1, 0], `if`(p<1, [0, 0],

      add((l->`if`(m=5, l+[0, l[1]*p], l))(b(n-p*m, p-1)), m=0..n/p)))

    end:

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

seq(a(n), n=5..55);

MATHEMATICA

b[n_, p_] := b[n, p] = If[n == 0 && p == 0, {1, 0}, If[p == 0, Array[0&, n+2], Sum[Function[l, ReplacePart[l, m+2 -> p*l[[1]] + l[[m+2]]]][Join[b[n-p*m, p-1], Array[0&, p*m]]], {m, 0, n/p}]]]; a[n_] := b[n, n][[7]]; Table[a[n], {n, 5, 55}] (* Jean-Fran├žois Alcover, Jan 24 2014, after Alois P. Heinz *)

CROSSREFS

Column k=5 of A222730.

Sequence in context: A299541 A066820 A309796 * A141677 A087459 A285103

Adjacent sequences:  A222730 A222731 A222732 * A222734 A222735 A222736

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Mar 03 2013

STATUS

approved

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Last modified September 24 14:46 EDT 2021. Contains 347643 sequences. (Running on oeis4.)