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A164864
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Number of ways of placing n labeled balls into 10 indistinguishable boxes; word structures of length n using a 10-ary alphabet.
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5
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1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678569, 4213530, 27641927, 190829797, 1381367941, 10448276360, 82285618467, 672294831619, 5676711562593, 49344452550230, 439841775811967, 4005444732928641
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..300
Moreira, N.; Reis, R. "On the Density of Languages Representing Finite Set Partitions", Journal of Integer Sequences, Vol. 8 (2005), Article 05.2.8.
Weisstein, Eric W. "Set Partition".
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FORMULA
| a(n) = Sum_{k=0..10} stirling2 (n,k).
a(n) = ceil (2119/11520*2^n +103/1680*3^n +53/3456*4^n +11/3600*5^n +6^n/1920 +7^n/15120 +8^n/80640 +10^n/3628800).
G.f.: (148329*x^9 -613453*x^8 +855652*x^7 -596229*x^6 +240065*x^5 -59410*x^4 +9177*x^3 -862*x^2 +45*x-1) / ((10*x-1) *(8*x-1) *(7*x-1) *(6*x-1) *(5*x-1) *(4*x-1) *(3*x-1) *(2*x-1) *(x-1)).
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MAPLE
| # First program:
a:= n-> ceil (2119/11520*2^n +103/1680*3^n +53/3456*4^n +11/3600*5^n +6^n/1920 +7^n/15120 +8^n/80640 +10^n/3628800): seq (a(n), n=0..25);
# 2nd program:
with (combinat): a:= n-> add (stirling2 (n, k), k=0..10): seq (a(n), n=0..25);
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CROSSREFS
| A000110, A048993, A008291, A098825, A000012, A000079, A007051, A007581, A124303, A056272, A056273, A099262, A099263, A164863.
Sequence in context: A192865 A164863 A192126 * A192866 A203641 A192127
Adjacent sequences: A164861 A164862 A164863 * A164865 A164866 A164867
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KEYWORD
| easy,nonn
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 28 2009
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