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A222709 Total number of parts of multiplicity 9 in all partitions of n. 2
1, 0, 1, 1, 2, 2, 4, 4, 7, 9, 13, 15, 23, 27, 38, 47, 63, 77, 104, 126, 165, 202, 259, 316, 403, 489, 614, 748, 929, 1125, 1391, 1676, 2055, 2475, 3012, 3613, 4379, 5233, 6306, 7521, 9018, 10717, 12805, 15171, 18050, 21337, 25288, 29806, 35221, 41400, 48760 (list; graph; refs; listen; history; text; internal format)
OFFSET

9,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 9..1000

FORMULA

G.f.: (x^9/(1-x^9)-x^10/(1-x^10))/Product_{j>0}(1-x^j).

a(n) ~ exp(Pi*sqrt(2*n/3)) / (180*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=9, 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=9..60);

MATHEMATICA

b[n_, p_] := b[n, p] = If[n == 0, {1, 0}, If[p < 1, {0, 0}, Sum[Function[l, If[m == 9, 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, 9, 60}] (* Jean-Fran├žois Alcover, Apr 30 2018, after Alois P. Heinz *)

CROSSREFS

Column k=9 of A197126.

Sequence in context: A206559 A143419 A183566 * A034396 A253412 A291148

Adjacent sequences:  A222706 A222707 A222708 * A222710 A222711 A222712

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 28 2013

STATUS

approved

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Last modified December 14 17:53 EST 2019. Contains 329979 sequences. (Running on oeis4.)