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A281688 Expansion of Sum_{i>=0} x^(2^i)/(1 - x^(2^i)) / Product_{j>=0} (1 - x^(2^j)). 3
1, 3, 5, 10, 14, 23, 29, 45, 55, 79, 93, 130, 150, 199, 225, 296, 332, 423, 469, 594, 654, 807, 881, 1085, 1179, 1423, 1537, 1850, 1990, 2355, 2521, 2983, 3185, 3719, 3957, 4618, 4902, 5655, 5985, 6909, 7299, 8343, 8793, 10050, 10574, 11979, 12577, 14260, 14952, 16823, 17609, 19818, 20718, 23155, 24169, 27033 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Total number of parts in all partitions of n into powers of 2 (A000079).
Convolution of A001511 and A018819.
LINKS
FORMULA
G.f.: Sum_{i>=0} x^(2^i)/(1 - x^(2^i)) / Product_{j>=0} (1 - x^(2^j)).
EXAMPLE
a(4) = 10 because we have [4], [2, 2], [2, 1, 1], [1, 1, 1, 1] and 1 + 2 + 3 + 4 = 10.
MAPLE
b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<0, 0, (p->
`if`(p>n, 0, (h-> h+[0, h[1]])(b(n-p, i))))(2^i)+b(n, i-1)))
end:
a:= n-> b(n, ilog2(n))[2]:
seq(a(n), n=1..56); # Alois P. Heinz, May 04 2021
MATHEMATICA
Rest[CoefficientList[Series[Sum[x^2^i/(1 - x^2^i), {i, 0, 20}]/Product[1 - x^2^j, {j, 0, 20}], {x, 0, 56}], x]]
CROSSREFS
Sequence in context: A176222 A365763 A008610 * A078411 A137630 A320886
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 27 2017
STATUS
approved

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Last modified June 23 04:27 EDT 2024. Contains 373629 sequences. (Running on oeis4.)