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.

A135756 a(n) = Sum_{k=0..n} C(n,k) * 2^(k*(k-1)).

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%I A135756 #17 Nov 27 2017 07:43:46
%S A135756 1,2,7,80,4381,1069742,1080096067,4405584869660,72092808533798521,
%T A135756 4723015159635987920282,1237987266193328694390243007,
%U A135756 1298087832233881093828346620725800
%N A135756 a(n) = Sum_{k=0..n} C(n,k) * 2^(k*(k-1)).
%C A135756 The square root of the g.f. of this sequence is an integer series (cf. A261594).
%H A135756 G. C. Greubel, <a href="/A135756/b135756.txt">Table of n, a(n) for n = 0..50</a>
%H A135756 Ville Salo, <a href="http://arxiv.org/abs/1411.6644">Decidability and Universality of Quasiminimal Subshifts</a>, arXiv:1411.6644 [math.DS], 2014-2015.
%F A135756 a(n) ~ 2^(n*(n-1)). - _Vaclav Kotesovec_, Nov 27 2017
%e A135756 G.f.: A(x) = 1 + 2*x + 7*x^2 + 80*x^3 + 4381*x^4 + 1069742*x^5 +...
%t A135756 Table[Sum[Binomial[n, k]*2^(2*Binomial[k, 2]), {k,0,n}], {n,0,25}] (* _G. C. Greubel_, Nov 07 2016 *)
%o A135756 (PARI) {a(n)=sum(k=0,n,binomial(n,k)*2^(k*(k-1)))}
%Y A135756 Cf. A261594; variants: A006896, A135755.
%K A135756 nonn
%O A135756 0,2
%A A135756 _Paul D. Hanna_, Nov 27 2007