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A222705 Total number of parts of multiplicity 5 in all partitions of n. 2
1, 0, 1, 1, 2, 3, 5, 5, 9, 11, 17, 21, 31, 37, 53, 67, 90, 113, 151, 186, 246, 305, 392, 486, 620, 762, 962, 1181, 1473, 1802, 2235, 2716, 3345, 4056, 4956, 5990, 7283, 8759, 10598, 12709, 15297, 18283, 21917, 26099, 31165, 37009, 44014, 52113, 61776, 72918 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 5..1000

FORMULA

G.f.: (x^5/(1-x^5)-x^6/(1-x^6))/Product_{j>0}(1-x^j).

a(n) ~ exp(Pi*sqrt(2*n/3)) / (60*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=5, 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=5..60);

MATHEMATICA

b[n_, p_] := b[n, p] = If[n == 0, {1, 0}, If[p < 1, {0, 0}, Sum[Function[l, If[m == 5, 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, 5, 60}] (* Jean-Fran├žois Alcover, Apr 30 2018, after Alois P. Heinz *)

CROSSREFS

Column k=5 of A197126.

Sequence in context: A091608 A317081 A183562 * A241381 A237365 A322770

Adjacent sequences:  A222702 A222703 A222704 * A222706 A222707 A222708

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 28 2013

STATUS

approved

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Last modified February 18 00:37 EST 2020. Contains 332006 sequences. (Running on oeis4.)