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A222734 Total sum of parts of multiplicity 6 in all partitions of n. 2
1, 0, 1, 1, 2, 2, 6, 6, 9, 12, 18, 22, 36, 43, 62, 77, 107, 133, 186, 229, 306, 384, 499, 621, 810, 999, 1277, 1582, 1997, 2453, 3088, 3776, 4698, 5742, 7088, 8618, 10592, 12824, 15654, 18910, 22955, 27615, 33400, 40028, 48174, 57593, 69018, 82231, 98225 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 6..1000

FORMULA

G.f.: (x^6/(1-x^6)^2-x^7/(1-x^7)^2)/Product_{i>=1}(1-x^i).

a(n) ~ 13 * sqrt(3) * exp(Pi*sqrt(2*n/3)) / (3528 * 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=6, 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=6..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][[8]]; Table[a[n], {n, 6, 55}] (* Jean-Fran├žois Alcover, Jan 24 2014, after Alois P. Heinz *)

CROSSREFS

Column k=6 of A222730.

Sequence in context: A010762 A055993 A309912 * A151888 A320046 A289835

Adjacent sequences:  A222731 A222732 A222733 * A222735 A222736 A222737

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Mar 03 2013

STATUS

approved

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Last modified September 22 19:36 EDT 2021. Contains 347608 sequences. (Running on oeis4.)