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

0,2

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).

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.

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);

Crossrefs

Column k=6 of A152977.

Sequence in context: A066278 A210773 A210774 * A210776 A210777 A210778

Adjacent sequences: A210772 A210773 A210774 * A210776 A210777 A210778

Keyword

nonn,easy

Author

Alois P. Heinz, Mar 26 2012

Status

approved