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A026815 Number of partitions of n in which the greatest part is 9. 12
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 41, 54, 73, 94, 123, 157, 201, 252, 318, 393, 488, 598, 732, 887, 1076, 1291, 1549, 1845, 2194, 2592, 3060, 3589, 4206, 4904, 5708, 6615, 7657, 8824, 10156, 11648, 13338, 15224 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,12

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 1..1000 from Vincenzo Librandi)

FORMULA

G.f.: x^9 / ((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)*(1-x^7)*(1-x^8)*(1-x^9)). [Colin Barker, Feb 22 2013]

a(n) = A008284(n,9). - Robert A. Russell, May 13 2018

MAPLE

part_ZL:=[S, {S=Set(U, card=r), U=Sequence(Z, card>=1)}, unlabeled]: seq(count(subs(r=9, part_ZL), size=m), m=1..50); # Zerinvary Lajos, Mar 09 2007

MATHEMATICA

Table[ Length[ Select[ Partitions[n], First[ # ] == 9 & ]], {n, 1, 60} ]

CoefficientList[Series[x^9/((1 - x) (1 - x^2) (1 - x^3) (1 - x^4) (1 - x^5) (1 - x^6) (1 - x^7) (1 - x^8) (1 - x^9)), {x, 0, 60}], x] (* Vincenzo Librandi, Oct 18 2013 *)

Drop[LinearRecurrence[{1, 1, 0, 0, -1, 0, -1, 0, 0, -1, 0, 2, 1, 1, 1, 0,

  -1, -1, -1, -2, -1, -1, 1, 1, 2, 1, 1, 1, 0, -1, -1, -1, -2, 0, 1, 0, 0,

1, 0, 1, 0, 0, -1, -1, 1}, Append[Table[0, {44}], 1], 136], 35] (* Robert A. Russell, May 17 2018 *)

PROG

(PARI) x='x+O('x^99); concat(vector(9), Vec(x^9/prod(k=1, 9, 1-x^k))) \\ Altug Alkan, May 17 2018

(GAP) List([0..70], n->NrPartitions(n, 9)); # Muniru A Asiru, May 17 2018

CROSSREFS

Essentially same as A008638.

Cf. A026810, A026811, A026812, A026813, A026814, A026816.

Sequence in context: A209039 A182805 A218509 * A008638 A008632 A238867

Adjacent sequences:  A026812 A026813 A026814 * A026816 A026817 A026818

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

EXTENSIONS

a(0)=0 prepended by Seiichi Manyama, Jun 08 2017

STATUS

approved

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Last modified January 19 17:45 EST 2019. Contains 319309 sequences. (Running on oeis4.)