A194197 Number of partitions of 60n into parts <= 6.

1, 19858, 436140, 2897747, 11402579, 33377536, 80758518, 171070425, 328507157, 585011614, 981355696, 1568220303, 2407275335, 3572259692, 5150061274, 7241796981, 9963892713, 13449163370, 17847892852, 23328914059, 30080688891, 38312388248, 48254972030, 60162269137

Offset: 0

Author

Adi Dani, Aug 21 2011

Keywords

• nonn
• easy

Comments

Number of partitions of 60n+k, 0<=k<60 into parts <=6 is a polynomial of degree 5 by variable n.

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A001402.

Programs

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 *)

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]