A210774 Number of partitions of 2^n into powers of 2 less than or equal to 32.

1, 2, 4, 10, 36, 202, 1827, 25509, 497097, 12070289, 333620001, 9898583617, 304816671873, 9567029991681, 303182221750785, 9654673365689345, 308196987575257089, 9850278328626941953, 315016627560700387329, 10077456621734453460993, 322429412555504845881345

Offset: 0

Author

Alois P. Heinz, Mar 26 2012

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (63, -1302, 11160, -41664, 64512, -32768).

Crossrefs

Column k=5 of A152977.

Programs

Maple

a:= n-> `if`(n<5, [1, 2, 4, 10, 36][n+1], (Matrix(6, (i, j)-> `if`(i=j-1, 1, `if`(i=6, [-32768, 64512, -41664, 11160, -1302, 63][j], 0)))^(n-5). <<202, 1827, 25509, 497097, 12070289, 333620001>>)[1,1]): seq(a(n), n=0..20);

Formula

G.f.: -(2048*x^9 -320*x^8 +4220*x^7 +5227*x^6 +14870*x^5 -23958*x^4 +8798*x^3 -1180*x^2 +61*x -1) / Product_{j=0..5} (2^j*x-1).

a(n) = [x^2^(n-1)] 1/(1-x) * 1/Product_{j=0..4} (1-x^(2^j)) for n>0.