cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A135068 a(n) = [x^(2^n+n-1)] (x + x^2 + x^4 + x^8 + ... + x^2^n)^n for n>=1.

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%I A135068 #20 Sep 11 2024 22:56:44
%S A135068 1,2,6,16,90,636,5712,34336,537282,5941780,99729146,1049982792,
%T A135068 23200347040,293841338896,5712436923000,68827002466176,
%U A135068 2844850573581890,53069160498788772,1545326270301621838,26021954987946879560,1020860369624228471394,19905401189634441143740,605270985059438427438138,11141784565490367848976336,621465511993167908247508400,14470690420043042111787089216,548187222712632324159956010732,11881058908943228840652007583056
%N A135068 a(n) = [x^(2^n+n-1)] (x + x^2 + x^4 + x^8 + ... + x^2^n)^n for n>=1.
%F A135068 a(n) = A135069(n)*n.
%t A135068 f[x_, n_] := (Sum[x^(2^k), {k, 0, n}])^n; Table[Coefficient[f[x, n], x^(2^n + n - 1)] , {n, 1, 20}] (* _G. C. Greubel_, Sep 22 2016 *)
%o A135068 (PARI) a(n)=if(n<1,0,polcoeff(sum(j=0,n,x^(2^j)+O(x^(2^n+n)))^n,2^n+n-1))
%Y A135068 Cf. A007178 (variant); A135069, A135070 (variant), A135071.
%K A135068 nonn
%O A135068 1,2
%A A135068 _Paul D. Hanna_, Nov 17 2007
%E A135068 a(15)-a(19) from _Alois P. Heinz_, Apr 29 2009
%E A135068 a(20)-a(22) from _Max Alekseyev_, Dec 03 2010
%E A135068 a(23)-a(28) from _Max Alekseyev_, Aug 31 2024