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.

A303649 Number of involutions of [n] having exactly one peak.

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%I A303649 #21 Sep 17 2019 17:56:48
%S A303649 0,0,0,1,6,18,44,91,172,300,496,781,1186,1742,2492,3479,4760,6392,
%T A303649 8448,11001,14142,17962,22572,28083,34628,42340,51376,61893,74074,
%U A303649 88102,104188,122543,143408,167024,193664,223601,257142,294594,336300,382603,433884,490524
%N A303649 Number of involutions of [n] having exactly one peak.
%H A303649 Alois P. Heinz, <a href="/A303649/b303649.txt">Table of n, a(n) for n = 0..20000</a>
%H A303649 Wikipedia, <a href="https://en.wikipedia.org/wiki/Involution_(mathematics)">Involution</a>
%H A303649 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-4,10,-4,-4,4,-1)
%F A303649 G.f.: x^3*(x^4-2*x^2+2*x+1)/((x+1)^2*(x-1)^6).
%e A303649 a(3) = 1: 132.
%e A303649 a(4) = 6: 1243, 1324, 1432, 2143, 3412, 4231.
%e A303649 a(5) = 18: 12354, 12435, 12543, 13245, 14325, 14523, 15432, 21354, 21435, 21543, 32154, 34125, 42315, 42513, 45312, 52341, 52431, 53241.
%t A303649 LinearRecurrence[{4,-4,-4,10,-4,-4,4,-1},{0,0,0,1,6,18,44,91},50] (* _Harvey P. Dale_, Sep 17 2019 *)
%Y A303649 Column k=1 of A303648.
%Y A303649 Cf. A000085.
%K A303649 nonn,easy
%O A303649 0,5
%A A303649 _Alois P. Heinz_, Apr 27 2018