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 A026816 Number of partitions of n in which the greatest part is 10. 24
 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 / (Product_{k=1..10} 1-x^k ). - Colin Barker, Feb 22 2013 a(n) = A008284(n,10). - Robert A. Russell, May 13 2018 a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} 1. - Wesley Ivan Hurt, Jul 13 2019 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 *) 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 (MAGMA) [#Partitions(k, 10): k in [1..51]]; // Marius A. Burtea, Jul 13 2019 CROSSREFS Essentially same as A008639. Cf. A026810, A026811, A026812, A026813, A026814, A026815. Sequence in context: A053691 A242696 A218510 * A008639 A341914 A008633 Adjacent sequences:  A026813 A026814 A026815 * A026817 A026818 A026819 KEYWORD nonn,easy AUTHOR EXTENSIONS a(0)=0 prepended by Seiichi Manyama, Jun 08 2017 STATUS approved

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Last modified September 28 04:53 EDT 2021. Contains 347703 sequences. (Running on oeis4.)