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A164863
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Number of ways of placing n labeled balls into 9 indistinguishable boxes; word structures of length n using a 9-ary alphabet.
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4
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1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115974, 678514, 4211825, 27602602, 190077045, 1368705291, 10254521370, 79527284317, 635182667816, 5199414528808, 43426867585575, 368654643520692, 3170300933550687, 27542984610086665, 241205285284001240
(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
Weisstein, Eric W. "Set Partition".
Moreira, N.; Reis, R. "On the Density of Languages Representing Finite Set Partitions", Journal of Integer Sequences, Vol. 8 (2005), Article 05.2.8.
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FORMULA
| a(n) = Sum_{k=0..9} stirling2 (n,k).
a(n) = ceil (103/560*2^n +53/864*3^n +11/720*4^n +5^n/320 +6^n/2160 +7^n/10080 +9^n/362880).
G.f.: (16687*x^8 -67113*x^7 +88620*x^6 -56993*x^5 +20529*x^4 -4353*x^3 +539*x^2 -36*x+1) / ((9*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 (103/560*2^n +53/864*3^n +11/720*4^n +5^n/320 +6^n/2160 +7^n/10080 +9^n/362880): seq (a(n), n=0..25);
# 2nd program:
with (combinat): a:= n-> add (stirling2 (n, k), k=0..9): seq (a(n), n=0..25);
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CROSSREFS
| Cf. A000110, A048993, A008291, A098825, A000012, A000079, A007051, A007581, A124303, A056272, A056273, A099262, A099263, A164864.
Sequence in context: A108305 A099263 A192865 * A192126 A164864 A192866
Adjacent sequences: A164860 A164861 A164862 * A164864 A164865 A164866
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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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