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A026813 Number of partitions of n in which the greatest part is 7. 13
0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 15, 21, 28, 38, 49, 65, 82, 105, 131, 164, 201, 248, 300, 364, 436, 522, 618, 733, 860, 1009, 1175, 1367, 1579, 1824, 2093, 2400, 2738, 3120, 3539, 4011, 4526, 5102, 5731, 6430, 7190, 8033, 8946, 9953, 11044, 12241 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

LINKS

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

FORMULA

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

a(n) = A008284(n,7). - Robert A. Russell, May 13 2018

MATHEMATICA

Table[ Length[ Select[ Partitions[n], First[ # ] == 7 & ]], {n, 1, 60} ]

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

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

  -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, -1, 1},

  Append[Table[0, {27}], 1], 121], 20] (* Robert A. Russell, May 17 2018 *)

PROG

(PARI) x='x+O('x^99); concat(vector(7), Vec(x^7/prod(k=1, 7, 1-x^k))) \\ Altug Alkan, May 17 2018

(GAP) List([0..70], n->NrPartitions(n, 7)); # Muniru A Asiru, May 17 2018

CROSSREFS

Cf. A026810, A026811, A026812, A026814, A026815, A026816.

Sequence in context: A049756 A319472 A218507 * A008636 A008630 A238865

Adjacent sequences:  A026810 A026811 A026812 * A026814 A026815 A026816

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Robert G. Wilson v, Jan 11 2002

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

STATUS

approved

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Last modified January 22 18:48 EST 2019. Contains 319365 sequences. (Running on oeis4.)