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A035927
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One less than number of n-multisets chosen from a 10-set.
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7
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0, 9, 54, 219, 714, 2001, 5004, 11439, 24309, 48619, 92377, 167959, 293929, 497419, 817189, 1307503, 2042974, 3124549, 4686824, 6906899, 10015004, 14307149, 20160074, 28048799, 38567099, 52451255, 70607459, 94143279
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OFFSET
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0,2
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COMMENTS
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Number of distinct n-digit numbers up to permutations of digits. - Michael Somos, Jul 11 2002
Equivalently, for n > 0, a(n) = number of n-digit decimal numbers d_1 d_2 ... d_n with d_1 > 0 and d_1 >= d_2 >= ... >= d_n >= 0.. - N. J. A. Sloane, Jul 13 2023
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LINKS
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Michael Beeler, R. William Gosper and Richard C. Schroeppel, HAKMEM, ITEM 56, Cambridge, MA: Mass. Institute of Technology Artificial Intelligence Laboratory, Memo AIM-239, Feb. 1972, Item 56.
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
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FORMULA
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MAPLE
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binomial(10+n-1, n)-1;
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MATHEMATICA
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CoefficientList[Series[1/(1-x)^10-1/(1-x), {x, 0, 30}], x] (* or *) LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 9, 54, 219, 714, 2001, 5004, 11439, 24309, 48619}, 30] (* Harvey P. Dale, Jul 11 2023 *)
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PROG
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(PARI) a(n)=if(n<0, 0, binomial(n+9, 9)-1)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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