

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
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OFFSET

9,5


LINKS

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


FORMULA

G.f.: (x^9/(1x^9)x^10/(1x^10))/Product_{j>0}(1x^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(np*m, p1)), 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}] (* JeanFrançois 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



