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 A026813 Number of partitions of n in which the greatest part is 7. 24
 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 a(n) = A008636(n-7). - R. J. Mathar, Feb 13 2019 a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3} Sum_{i=j..floor((n-j-k-l-m-o)/2)} 1. - Wesley Ivan Hurt, Jun 30 2019 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 (MAGMA) [#Partitions(n, 7): n in [0..53]]; // Marius A. Burtea, Jul 01 2019 CROSSREFS Cf. A026810, A026811, A026812, A026814, A026815, A026816. Sequence in context: A319472 A309099 A218507 * A008636 A008630 A238865 Adjacent sequences:  A026810 A026811 A026812 * A026814 A026815 A026816 KEYWORD nonn,easy AUTHOR 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 October 20 08:05 EDT 2019. Contains 328252 sequences. (Running on oeis4.)