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.

A135070 a(n) = [x^(2^n+n-2)] (x + x^2 + x^4 + x^8 + ... + x^(2^n))^n for n>=1.

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%I A135070 #18 Sep 11 2024 22:58:32
%S A135070 1,1,3,18,70,600,4956,52528,358128,6654600,79967800,1453049400,
%T A135070 16239408120,392541718660,5252687631660,108961629396480,
%U A135070 1395025456201408,62831427044385384,1223872353413404344,37391632408971430120,655014723078024641640,27055523795138159291124,547691411941958414420092,17365164578604322437671664,332211955074827711097949200,19385342415197943809053622700,466687147661484232610990714436,18326221432646410203582181439808
%N A135070 a(n) = [x^(2^n+n-2)] (x + x^2 + x^4 + x^8 + ... + x^(2^n))^n for n>=1.
%F A135070 n(n-1)/2 divides a(n) for n>=2: A135071(n) = a(n)/[n(n-1)/2] for n>=2.
%t A135070 f[x_, n_] := (Sum[x^(2^k), {k, 0, n}])^n; Table[Coefficient[f[x, n], x^(2^n + n - 2)] , {n, 2, 10}] (* _G. C. Greubel_, Sep 22 2016 *)
%o A135070 (PARI) {a(n)=if(n<2,0,polcoeff(sum(j=0,n,x^(2^j)+O(x^(2^n+n)))^n,2^n+n-2))}
%Y A135070 Cf. A135068, A135069, A135071.
%K A135070 nonn
%O A135070 1,3
%A A135070 _Paul D. Hanna_, Nov 17 2007
%E A135070 a(15)-a(19) from _Alois P. Heinz_, Apr 29 2009
%E A135070 a(1) prepended and a(20)-a(28) added by _Max Alekseyev_, Aug 31 2024