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 A026815 Number of partitions of n in which the greatest part is 9. 24
 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: A182805 A309058 A218509 * A008638 A008632 A238867 Adjacent sequences:  A026812 A026813 A026814 * A026816 A026817 A026818 KEYWORD nonn,easy AUTHOR EXTENSIONS a(0)=0 prepended by Seiichi Manyama, Jun 08 2017 STATUS approved

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Last modified June 2 14:21 EDT 2020. Contains 334787 sequences. (Running on oeis4.)