A210777 Number of partitions of 2^n into powers of 2 less than or equal to 256.

1, 2, 4, 10, 36, 202, 1828, 27338, 692004, 30251721, 2290267225, 275723872209, 45943934602273, 9336623954364993, 2119856439870545025, 510453118614955153665, 126696287737269468934657, 31933986928271408429425665, 8111646059635412792802330625

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..130

Index entries for linear recurrences with constant coefficients, signature (511, -86870, 6304280, -211823808, 3389180928, -25822330880, 91089797120, -137170518016, 68719476736).

Formula

G.f.: (54717883351040*x^16 -83085001490432*x^15 +28916158300160*x^14 -281547988992*x^13 -272750006528*x^12 +100712240*x^11 -7148051274*x^10 -10790841321*x^9 -30886151190*x^8 +51093934102*x^7 -19831247382*x^6 +2989899926*x^5 -199557654*x^4 +6132574*x^3 -85852*x^2 +509*x-1) / Product_{j=0..8} (2^j*x-1).

a(n) = [x^2^(n-1)] 1/(1-x) * 1/Product_{j=0..7} (1-x^(2^j)) for n>0.

Maple

gf:= (-1 +(509 +(-85852 +(6132574 +(-199557654 +(2989899926 +(-19831247382 +(51093934102 +(-30886151190 +(-10790841321 +(-7148051274 +(100712240 +(-272750006528 +(-281547988992 +(28916158300160 +(-83085001490432 +54717883351040*x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x)/ mul(2^j*x-1, j=0..8): a:= n-> coeff(series(gf, x, n+1), x, n): seq(a(n), n=0..20);

Crossrefs

Column k=8 of A152977.

Sequence in context: A210774 A210775 A210776 * A210778 A210779 A002577

Adjacent sequences: A210774 A210775 A210776 * A210778 A210779 A210780

Keyword

nonn,easy

Author

Alois P. Heinz, Mar 26 2012

Status

approved