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A194197 Number of partitions of 60n into parts <= 6. 1
1, 19858, 436140, 2897747, 11402579, 33377536, 80758518, 171070425, 328507157, 585011614, 981355696, 1568220303, 2407275335, 3572259692, 5150061274, 7241796981, 9963892713, 13449163370, 17847892852, 23328914059, 30080688891, 38312388248, 48254972030, 60162269137 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Number of partitions of 60n+k, 0<=k<60 into parts <=6 is a polynomial of degree 5 by variable n.
LINKS
FORMULA
a(n) = 1 +(167*n +2325*n^2 +15400*n^3 +47250*n^4 +54000*n^5)/6.
a(n) = A001402(60*n).
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]
MATHEMATICA
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 *)
CROSSREFS
Cf. A001402.
Sequence in context: A206508 A206058 A236497 * A250703 A256653 A186957
KEYWORD
nonn,easy
AUTHOR
Adi Dani, Aug 21 2011
STATUS
approved

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Last modified May 21 00:14 EDT 2024. Contains 372720 sequences. (Running on oeis4.)