A238633 Number of partitions of 6^n into parts that are at most 6.

1, 11, 2432, 6889527, 44056912182, 331281477244572, 2561606354507677872, 19900384510848921094632, 154721208025657067873668152, 1203080775953722005263023646232, 9355115500676554620340590943203672, 72745325498731282220397926627254957272

Offset: 0

Author

Alois P. Heinz, Mar 01 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..250

Crossrefs

Row n=6 of A238016.

Programs

Maple

gf:= -(29386561536*x^7 [phone]*x^6 [phone]*x^5 -77061923145*x^4 [phone]*x^3 -12336681*x^2+9320*x-1)/ mul(1-6^j*x, j=0..5):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..20);

Formula

a(n) = [x^(6^n)] Product_{j=1..6} 1/(1-x^j).

G.f.: -(29386561536*x^7 [phone]*x^6 [phone]*x^5 -77061923145*x^4 [phone]*x^3 -12336681*x^2 +9320*x-1) / Product_{j=0..5} 1-6^j*x.