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Expansion of 1/Product_{ n >= 2, n not of the form 2^k-1 } (1 - x^n).
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%I #28 Oct 25 2024 10:04:03

%S 1,0,1,0,2,1,3,1,5,3,8,5,12,9,18,14,27,23,40,35,58,54,84,80,120,118,

%T 170,171,239,246,334,347,463,489,638,680,873,940,1189,1288,1609,1755,

%U 2167,2374,2903,3196,3872,4275,5140,5692,6795,7540,8944,9945,11729,13057,15321,17077

%N Expansion of 1/Product_{ n >= 2, n not of the form 2^k-1 } (1 - x^n).

%C a(n) counts the partitions of n where no part has the form 2^k - 1 for a positive integer k. - _Brian Hopkins_, Jul 21 2017

%C a(n) is the dimension of the n-th unoriented bordism group as a Z_2-module. - _Milan Zerbin_, Oct 03 2024

%H A. Dold, <a href="https://doi.org/10.1007/BF01473868">Erzeugende der Thomschen Algebra N</a>, Math Z 65, 25-35 (1956).

%e The a(9) = 3 allowed partitions of 9 are (9), (5,4), and (5,2,2).

%o (PARI) isok(p) = {for (i=1, #p, if ((p[i]==1) || (ispower(p[i]+1,,&t) && (t==2)), return (0));); return(1);}

%o a(n) = {my(nb = 0); forpart(p=n, nb += isok(p);); nb;} \\ _Michel Marcus_, Jul 22 2017

%Y Cf. A078658.

%K nonn

%O 0,5

%A _N. J. A. Sloane_, Dec 15 2002