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A222735 Total sum of parts of multiplicity 7 in all partitions of n. 2
1, 0, 1, 1, 2, 2, 4, 6, 9, 10, 16, 20, 29, 36, 53, 66, 91, 112, 152, 190, 251, 315, 409, 510, 655, 809, 1029, 1271, 1602, 1967, 2457, 3009, 3729, 4543, 5595, 6801, 8321, 10069, 12258, 14783, 17906, 21511, 25947, 31073, 37315, 44542, 53285, 63415, 75587, 89687 (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)^2-x^8/(1-x^8)^2)/Product_{i>=1}(1-x^i).

a(n) ~ 15 * sqrt(3) * exp(Pi*sqrt(2*n/3)) / (6272 * 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=7, 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=7..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][[9]]; Table[a[n], {n, 7, 60}] (* Jean-Fran├žois Alcover, Jan 24 2014, after Alois P. Heinz *)

CROSSREFS

Column k=7 of A222730.

Sequence in context: A091966 A231187 A055529 * A299408 A319381 A035564

Adjacent sequences:  A222732 A222733 A222734 * A222736 A222737 A222738

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Mar 03 2013

STATUS

approved

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Last modified February 24 17:00 EST 2020. Contains 332209 sequences. (Running on oeis4.)