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A026816 Number of partitions of n in which the greatest part is 10. 12
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 55, 75, 97, 128, 164, 212, 267, 340, 423, 530, 653, 807, 984, 1204, 1455, 1761, 2112, 2534, 3015, 3590, 4242, 5013, 5888, 6912, 8070, 9418, 10936, 12690, 14663, 16928, 19466 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,13

LINKS

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

FORMULA

G.f.: x^10 / ((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)*(1-x^10)). - Colin Barker, Feb 22 2013

a(n) = a(n-1) + a(n-2) - a(n-5) - a(n-7) - a(n-11) + a(n-12) + a(n-13) + a(n-14) + 2*a(n-15) - a(n-18) - a(n-19) - a(n-20) - a(n-21) - 3*a(n-22) + a(n-25) + a(n-26) + 2*a(n-27) + 2*a(n-28) + a(n-29) + a(n-30) - 3*a(n-33) - a(n-34) - a(n-35) - a(n-36) - a(n-37) + 2*a(n-40) + a(n-41) + a(n-42) + a(n-43) - a(n-44) - a(n-48) - a(n-50) + a(n-53) + a(n-54) - a(n-55). - David Neil McGrath, Jul 26 2015

a(n) = A008284(n,10). - Robert A. Russell, May 13 2018

MATHEMATICA

Table[ Length[ Select[ Partitions[n], First[ # ] == 10 & ]], {n, 1, 60} ]

CoefficientList[Series[x^10/((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) (1 - x^10)), {x, 0, 60}], x] (* Vincenzo Librandi, Oct 18 2013 *)

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

  0, -1, -1, -1, -1, -3, 0, 0, 1, 1, 2, 2, 1, 1, 0,  0, -3, -1, -1, -1,

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

Append[Table[0, {54}], 1], 145], 44] (* Robert A. Russell, May 17 2018 *)

PROG

(PARI) concat(vector(9), Vec(1/prod(k=1, 10, 1-x^k)+O(x^90))) \\ Charles R Greathouse IV, May 06 2015

(GAP) List([0..70], n->NrPartitions(n, 10)); # Muniru A Asiru, May 17 2018

CROSSREFS

Essentially same as A008639.

Cf. A026810, A026811, A026812, A026813, A026814, A026815.

Sequence in context: A053691 A242696 A218510 * A008639 A008633 A238868

Adjacent sequences:  A026813 A026814 A026815 * A026817 A026818 A026819

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 December 15 20:33 EST 2018. Contains 318154 sequences. (Running on oeis4.)