A210775 Number of partitions of 2^n into powers of 2 less than or equal to 64.

1, 2, 4, 10, 36, 202, 1828, 27337, 664665, 23693265, 1092226081, 58686573121, 3431048928385, 209706732148993, 13113096655221249, 829504773400454145, 52778852611947546625, 3367976225848670392321, 215235141069830389702657, 13764966441742878856593409

Offset: 0

Author

Alois P. Heinz, Mar 26 2012

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..175
• Index entries for linear recurrences with constant coefficients, signature (127, -5334, 94488, -755904, 2731008, -4161536, 2097152).

Crossrefs

Column k=6 of A152977.

Programs

Maple

a:= n-> `if`(n<7, [1, 2, 4, 10, 36, 202, 1828][n+1], (Matrix(7, (i, j)-> `if`(i=j-1, 1, `if`(i=7, [2097152, -4161536, 2731008, -755904, 94488, -5334, 127][j], 0)))^(n-6). <<1828, 27337, 664665, 23693265, 1092226081, 58686573121, 3431048928385>>)[1,1]): seq(a(n), n=0..20);

Formula

G.f.: -(7864320*x^12 -12132352*x^11 +4458752*x^10 -24624*x^9 +211146*x^8 +332009*x^7 +946454*x^6 -1548182*x^5 +587030*x^4 -84318*x^3 +5084*x^2 -125*x+1) / Product_{j=0..6} (2^j*x-1).

a(n) = [x^2^(n-1)] 1/(1-x) * 1/Product_{j=0..5} (1-x^(2^j)) for n>0.