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A212549 Number of partitions of n containing at least one part m-9 if m is the largest part. 2
0, 0, 1, 1, 3, 4, 8, 11, 19, 26, 41, 56, 83, 111, 158, 209, 287, 375, 503, 648, 852, 1086, 1403, 1770, 2255, 2817, 3546, 4393, 5469, 6723, 8294, 10120, 12382, 15011, 18228, 21965, 26497, 31749, 38069, 45383, 54114, 64204, 76176, 89975, 106259, 124998, 146987 (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.: Sum_{i>0} x^(2*i+9) / Product_{j=1..9+i} (1-x^j).

EXAMPLE

a(11) = 1: [10,1].

a(12) = 1: [10,1,1].

a(13) = 3: [10,1,1,1], [10,2,1], [11,2].

a(14) = 4: [10,1,1,1,1], [10,2,1,1], [10,3,1], [11,2,1].

a(15) = 8: [10,1,1,1,1,1], [10,2,1,1,1], [10,2,2,1], [10,3,1,1], [10,4,1], [11,2,1,1], [11,2,2], [12,3].

MAPLE

b:= proc(n, i) option remember;

      `if`(n=0 or i=1, 1, b(n, i-1)+`if`(i>n, 0, b(n-i, i)))

    end:

a:= n-> add(b(n-2*m-9, min(n-2*m-9, m+9)), m=1..(n-9)/2):

seq(a(n), n=9..60);

CROSSREFS

Column k=9 of A212551.

Sequence in context: A212546 A212547 A212548 * A212550 A024786 A299069

Adjacent sequences:  A212546 A212547 A212548 * A212550 A212551 A212552

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 20 2012

STATUS

approved

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Last modified April 20 14:27 EDT 2019. Contains 322310 sequences. (Running on oeis4.)