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 A008640 Number of partitions of n into at most 11 parts. 3

%I

%S 1,1,2,3,5,7,11,15,22,30,42,56,76,99,131,169,219,278,355,445,560,695,

%T 863,1060,1303,1586,1930,2331,2812,3370,4035,4802,5708,6751,7972,9373,

%U 11004,12866,15021,17475,20298,23501,27169,31316,36043,41373,47420,54218,61903,70515,80215,91058,103226,116792,131970,148847

%N Number of partitions of n into at most 11 parts.

%C For n>10: also number of partitions of n into parts <= 11: a(n)=A026820(n,11). [_Reinhard Zumkeller_, Jan 21 2010]

%D A. Cayley, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 10, p. 415.

%D H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, Vol. 4, Cambridge Univ. Press, 1958, p. 2.

%H T. D. Noe, <a href="/A008640/b008640.txt">Table of n, a(n) for n = 0..1000</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=360">Encyclopedia of Combinatorial Structures 360</a>

%H <a href="/index/Rec#order_66">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, -1, -1, -1, -2, -1, -1, 0, -1, 2, 2, 2, 2, 1, 1, 0, -1, -1, -2, -2, -2, -2, 1, 0, 1, 1, 2, 1, 1, 1, 0, 0, -1, -2, -1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, -1, -1, 1).

%F a(n) = a(n-1) + a(n-2) - a(n-5) - a(n-7) + a(n-14) + 2*a(n-15) + a(n-16) - a(n-19) - a(n-20) - a(n-21) - 2*a(n-22) - a(n-23) - a(n-24) - a(n-26) + 2*a(n-27) + 2*a(n-28) + 2*a(n-29) + 2*a(n-30) + a(n-31) + a(n-32) - a(n-34) - a(n-35) - 2*a(n-36) - 2*a(n-37) - 2*a(n-38) - 2*a(n-39) + a(n-40) + a(n-42) + a(n-43) + 2*a(n-44) + a(n-45) + a(n-46) + a(n-47) - a(n-50) - 2*a(n-51) - a(n-52) + a(n-59) + a(n-61) - a(n-64) - a(n-65) + a(n-66). - _David Neil McGrath_, Jul 27 2015

%F G.f.: 1 / prod(k=1..11, 1 - x^k ). - _Joerg Arndt_, Aug 04 2015

%p 1/(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)/(1-x^11)

%p with(combstruct):ZL12:=[S,{S=Set(Cycle(Z,card<12))},unlabeled]: seq(count(ZL12,size=n),n=0..44); # _Zerinvary Lajos_, Sep 24 2007

%p B:=[S,{S = Set(Sequence(Z,1 <= card),card <=11)},unlabelled]: seq(combstruct[count](B, size=n), n=0..44); # _Zerinvary Lajos_, Mar 21 2009

%t CoefficientList[ Series[ 1/ Product[ 1 - x^n, {n, 1, 11} ], {x, 0, 60} ], x ]

%Y Differs from A008634 at 55th term.

%Y a(n) = A008284(n+11, 11), n >= 0.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_

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Last modified May 17 12:55 EDT 2021. Contains 343971 sequences. (Running on oeis4.)