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A212550 Number of partitions of n containing at least one part m-10 if m is the largest part. 2
0, 0, 1, 1, 3, 4, 8, 11, 19, 26, 41, 56, 83, 112, 159, 211, 291, 381, 512, 663, 873, 1117, 1448, 1833, 2342, 2938, 3708, 4611, 5760, 7105, 8792, 10769, 13215, 16077, 19585, 23679, 28651, 34447, 41424, 49541, 59248, 70509, 83892, 99390, 117695, 138846, 163708 (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.: Sum_{i>0} x^(2*i+10) / Product_{j=1..10+i} (1-x^j).

EXAMPLE

a(12) = 1: [11,1].

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

a(14) = 3: [11,1,1,1], [11,2,1], [12,2].

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

a(16) = 8: [11,1,1,1,1,1], [11,2,1,1,1], [11,2,2,1], [11,3,1,1], [11,4,1], [12,2,1,1], [12,2,2], [13,3].

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-10, min(n-2*m-10, m+10)), m=1..(n-10)/2):

seq(a(n), n=10..60);

MATHEMATICA

Table[Count[IntegerPartitions[n], _?(MemberQ[#, #[[1]]-10]&)], {n, 10, 60}] (* Harvey P. Dale, Feb 10 2015 *)

CROSSREFS

Column k=10 of A212551.

Sequence in context: A212547 A212548 A212549 * A024786 A299069 A097497

Adjacent sequences:  A212547 A212548 A212549 * A212551 A212552 A212553

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 20 2012

STATUS

approved

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Last modified April 18 13:05 EDT 2019. Contains 322209 sequences. (Running on oeis4.)