A210776 Number of partitions of 2^n into powers of 2 less than or equal to 128.

1, 2, 4, 10, 36, 202, 1828, 27338, 692003, 29559717, 1933411785, 169368653201, 17695666168609, 2038699559609921, 247324139826203777, 30811717563505088769, 3890604470232727499265, 494612931489164269609985, 63094694253683687355107329

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..150

Index entries for linear recurrences with constant coefficients, signature (255, -21590, 777240, -12850368, 99486720, -353730560, 534773760, -268435456).

Formula

G.f.: (4009754624*x^13 -4990304256*x^12 +1018234880*x^11 -57698752*x^10 -28134460*x^9 -42258923*x^8 -120814102*x^7 +199113750*x^6 -76688022*x^5 +11379734*x^4-735070*x^3+21084*x^2-253*x+1)/Product_{j=0..7} (2^j*x-1).

a(n) = [x^2^(n-1)] 1/(1-x) * 1/Product_{j=0..6} (1-x^(2^j)) for n>0.

Maple

gf:= (1 +(-253 +(21084 +(-735070 +(11379734 +(-76688022 +(199113750 +(-120814102 +(-42258923 +(-28134460 +(-57698752+(1018234880 +(-4990304256 +4009754624*x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x)/ mul(2^j*x-1, j=0..7): a:= n-> coeff(series(gf, x, n+1), x, n): seq(a(n), n=0..20);

Crossrefs

Column k=7 of A152977.

Sequence in context: A210773 A210774 A210775 * A210777 A210778 A210779

Adjacent sequences: A210773 A210774 A210775 * A210777 A210778 A210779

Keyword

nonn,easy

Author

Alois P. Heinz, Mar 26 2012

Status

approved