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A222710 Total number of parts of multiplicity 10 in all partitions of n. 2
1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 13, 15, 22, 26, 37, 45, 61, 74, 99, 120, 158, 192, 247, 300, 382, 463, 582, 705, 877, 1059, 1309, 1575, 1931, 2319, 2823, 3381, 4094, 4886, 5886, 7007, 8401, 9971, 11905, 14090, 16756, 19781, 23436, 27594, 32586, 38268, 45050 (list; graph; refs; listen; history; text; internal format)
OFFSET

10,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 10..1000

FORMULA

G.f.: (x^10/(1-x^10)-x^11/(1-x^11))/Product_{j>0}(1-x^j).

a(n) ~ exp(Pi*sqrt(2*n/3)) / (220*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=10, 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=10..60);

MATHEMATICA

b[n_, p_] := b[n, p] = If[n == 0, {1, 0}, If[p < 1, {0, 0}, Sum[Function[l, If[m == 10, 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, 10, 60}] (* Jean-Fran├žois Alcover, Apr 30 2018, after Alois P. Heinz *)

CROSSREFS

Column k=10 of A197126.

Sequence in context: A206560 A035554 A183567 * A032278 A222738 A005308

Adjacent sequences:  A222707 A222708 A222709 * A222711 A222712 A222713

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 28 2013

STATUS

approved

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Last modified December 8 01:59 EST 2019. Contains 329850 sequences. (Running on oeis4.)