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A289842
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Sum of products of terms in all partitions of 2*n into powers of 2.
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3
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1, 3, 11, 27, 83, 195, 515, 1155, 2899, 6387, 15219, 32883, 76275, 163059, 368883, 780531, 1738259, 3653715, 8022355, 16759635, 36428371, 75765843, 163217491, 338120787, 723384915, 1493913171, 3176799827, 6542573139, 13844246099, 28447592019, 59934789203
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = [x^(2*n)] Product_{k>=0} 1/(1 - 2^k*x^(2^k)). - Ilya Gutkovskiy, Sep 10 2018
a(n) ~ c * n * 2^n, where c = 2.1343755406794500897789546611306737041750472866941557748356... - Vaclav Kotesovec, Jun 18 2019
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EXAMPLE
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n | partitions of 2*n into powers of 2 | a(n)
--------------------------------------------------------------------------
1 | 2 , 1+1 | 2+1 = 3.
2 | 4 , 2+2 , 2+1+1, 1+1+1+1 | 4+4+2+1 = 11.
3 | 4+2, 4+1+1, 2+2+2, 2+2+1+1, 2+1+1+1+1, 1+1+1+1+1+1 | 8+4+8+4+2+1 = 27.
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MAPLE
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b:= proc(n, i, p) option remember; `if`(n=0, p,
`if`(i<1, 0, add(b(n-j*i, i/2, p*i^j), j=0..n/i)))
end:
a:= n-> (t-> b(t, 2^ilog2(t), 1))(2*n):
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MATHEMATICA
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b[n_, i_, p_] := b[n, i, p] = If[n == 0, p, If[i < 1, 0, Sum[b[n - j i, i/2, p i^j], {j, 0, n/i}]]];
a[n_] := b[2n, 2^Floor@Log[2, 2n], 1];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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