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
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).
Crossrefs
Column k=7 of A152977.
Programs
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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);
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.