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
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).
Crossrefs
Column k=8 of A152977.
Programs
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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);
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.