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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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9
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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, 37136385907400125, 349459367068932740
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{k=0..10} Stirling2 (n,k).
a(n) = ceiling(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
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# 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);
# second program:
a:= n-> add(Stirling2(n, k), k=0..10): seq(a(n), n=0..25);
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MATHEMATICA
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Table[Sum[StirlingS2[n, k], {k, 0, 10}], {n, 0, 30}] (* Harvey P. Dale, Nov 22 2023 *)
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CROSSREFS
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Cf. A000110, A048993, A008291, A098825, A000012, A000079, A007051, A007581, A124303, A056272, A056273, A099262, A099263, A164863.
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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