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A222707 Total number of parts of multiplicity 7 in all partitions of n. 2
1, 0, 1, 1, 2, 2, 4, 5, 8, 9, 14, 17, 25, 30, 43, 53, 72, 88, 118, 145, 190, 234, 301, 370, 471, 575, 724, 884, 1102, 1339, 1657, 2007, 2465, 2975, 3630, 4369, 5301, 6355, 7672, 9171, 11018, 13126, 15706, 18655, 22231, 26329, 31260, 36920, 43688, 51454, 60693 (list; graph; refs; listen; history; text; internal format)
OFFSET

7,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 7..1000

FORMULA

G.f.: (x^7/(1-x^7)-x^8/(1-x^8))/Product_{j>0}(1-x^j).

a(n) ~ exp(Pi*sqrt(2*n/3)) / (112*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=7, 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=7..60);

MATHEMATICA

b[n_, p_] := b[n, p] = If[n == 0, {1, 0}, If[p < 1, {0, 0}, Sum[Function[l, If[m == 7, 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, 7, 60}] (* Jean-Fran├žois Alcover, Apr 30 2018, after Alois P. Heinz *)

CROSSREFS

Column k=7 of A197126.

Sequence in context: A069906 A304332 A183564 * A326525 A326630 A317810

Adjacent sequences:  A222704 A222705 A222706 * A222708 A222709 A222710

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 28 2013

STATUS

approved

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Last modified January 27 17:58 EST 2020. Contains 331296 sequences. (Running on oeis4.)