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A289842 Sum of products of terms in all partitions of 2*n into powers of 2. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..3309

FORMULA

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

EXAMPLE

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.

MAPLE

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):

seq(a(n), n=0..33);  # Alois P. Heinz, Oct 27 2017

MATHEMATICA

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];

a /@ Range[0, 33] (* Jean-Fran├žois Alcover, Nov 23 2020, after Alois P. Heinz *)

CROSSREFS

Cf. A000123, A018819.

Sequence in context: A059400 A250223 A250271 * A077776 A113836 A036571

Adjacent sequences:  A289839 A289840 A289841 * A289843 A289844 A289845

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Oct 27 2017

STATUS

approved

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Last modified October 23 12:42 EDT 2021. Contains 348214 sequences. (Running on oeis4.)