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A222736 Total sum of parts of multiplicity 8 in all partitions of n. 2
1, 0, 1, 1, 2, 2, 4, 4, 9, 10, 14, 18, 27, 32, 46, 57, 80, 99, 134, 163, 219, 270, 350, 433, 561, 686, 875, 1074, 1349, 1652, 2062, 2509, 3116, 3783, 4650, 5633, 6893, 8305, 10108, 12153, 14709, 17630, 21243, 25371, 30452, 36271, 43335, 51478, 61311, 72598 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 8..1000

FORMULA

G.f.: (x^8/(1-x^8)^2-x^9/(1-x^9)^2)/Product_{i>=1}(1-x^i).

a(n) ~ 17 * sqrt(3) * exp(Pi*sqrt(2*n/3)) / (10368 * 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=8, 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=8..60);

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][[10]]; Table[a[n], {n, 8, 60}] (* Jean-Fran├žois Alcover, Jan 24 2014, after Alois P. Heinz *)

CROSSREFS

Column k=8 of A222730.

Sequence in context: A322112 A324409 A110199 * A053656 A035054 A099537

Adjacent sequences:  A222733 A222734 A222735 * A222737 A222738 A222739

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Mar 03 2013

STATUS

approved

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Last modified February 25 04:32 EST 2020. Contains 332217 sequences. (Running on oeis4.)