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A222708 Total number of parts of multiplicity 8 in all partitions of n. 2
1, 0, 1, 1, 2, 2, 4, 4, 8, 9, 13, 16, 24, 28, 40, 49, 67, 82, 110, 133, 176, 215, 276, 338, 432, 524, 661, 804, 1001, 1214, 1502, 1812, 2228, 2683, 3270, 3928, 4766, 5699, 6879, 8208, 9855, 11724, 14020, 16624, 19804, 23423, 27788, 32781, 38770, 45603, 53762 (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)-x^9/(1-x^9))/Product_{j>0}(1-x^j).

a(n) ~ exp(Pi*sqrt(2*n/3)) / (144*Pi*sqrt(2*n)). - Vaclav Kotesovec, May 24 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]], 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, {1, 0}, If[p < 1, {0, 0}, Sum[Function[l, If[m == 8, l + {0, l[[1]]}, l]][b[n - p*m, p - 1]], {m, 0, n/p}]]];

a[n_] := b[n, n][[2]];

Table[a[n], {n, 8, 60}] (* Jean-Fran├žois Alcover, Apr 30 2018, after Alois P. Heinz *)

CROSSREFS

Column k=8 of A197126.

Sequence in context: A217208 A287136 A183565 * A324843 A306692 A120803

Adjacent sequences:  A222705 A222706 A222707 * A222709 A222710 A222711

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 28 2013

STATUS

approved

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Last modified January 25 03:49 EST 2020. Contains 331241 sequences. (Running on oeis4.)