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A194197
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Number of partitions of 60n into parts <= 6.
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1
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1, 19858, 436140, 2897747, 11402579, 33377536, 80758518, 171070425, 328507157, 585011614, 981355696, 1568220303, 2407275335, 3572259692, 5150061274, 7241796981, 9963892713, 13449163370, 17847892852, 23328914059, 30080688891, 38312388248, 48254972030, 60162269137
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OFFSET
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0,2
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COMMENTS
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Number of partitions of 60n+k, 0<=k<60 into parts <=6 is a polynomial of degree 5 by variable n.
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LINKS
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FORMULA
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a(n) = 1 +(167*n +2325*n^2 +15400*n^3 +47250*n^4 +54000*n^5)/6.
G.f.: (3331*x^5+161052*x^4+578757*x^3+317007*x^2+19852*x+1)/(x-1)^6. [Colin Barker, Jan 31 2013]
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MATHEMATICA
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Table[1 + (167n + 2325n^2 + 15400n^3 + 47250n^4 + 54000n^5)/6, {n, 0, 25}]
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 19858, 436140, 2897747, 11402579, 33377536}, 30] (* Harvey P. Dale, Aug 12 2018 *)
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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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