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A026815
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Number of partitions of n in which the greatest part is 9.
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24
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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, 17354, 19720, 22380
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OFFSET
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0,12
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (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).
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FORMULA
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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
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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