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.

A136284 Number of graphs on n labeled nodes with maximal degree exactly 2.

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%I A136284 #17 Jul 24 2016 20:15:19
%S A136284 0,0,4,31,227,1782,15564,151455,1635703,19457998,252962528,3568119351,
%T A136284 54262590843,884831668974,15397747311556,284767367151241,
%U A136284 5576696534340377,115269731259650802,2507575460681918232,57262481202198407625,1369461739333488200365
%N A136284 Number of graphs on n labeled nodes with maximal degree exactly 2.
%D A136284 D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.
%H A136284 Alois P. Heinz, <a href="/A136284/b136284.txt">Table of n, a(n) for n = 1..200</a>
%F A136284 Equals A136281 - A000085.
%F A136284 Recurrence: 2*(n-3)*(9*n-64)*a(n) = 2*(18*n^3 - 182*n^2 + 423*n - 149)*a(n-1) - 2*(n-1)*(9*n^3 - 91*n^2 + 243*n - 173)*a(n-2) + 6*(n-2)*(n-1)*(n+1)*a(n-3) + (n-3)*(n-2)*(n-1)*(9*n^2 - 91*n + 224)*a(n-4) - (n-4)*(n-3)*(n-2)*(n-1)*(9*n-67)*a(n-5) + (n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(9*n-55)*a(n-6). - _Vaclav Kotesovec_, Feb 09 2014
%F A136284 a(n) ~ exp(sqrt(2*n)-n-1/2) * n^n / sqrt(2) * (1 + 19/(24*sqrt(2*n))). - _Vaclav Kotesovec_, Feb 09 2014
%F A136284 E.g.f.: exp(1/(1-x)/2 - 1/2 + log(1/(1-x))/2-x^2/4) - exp(x+x^2/2!). - _Joerg Arndt_, Jul 24 2016
%t A136284 nn = 20; Drop[Range[0, nn]! CoefficientList[Series[Exp[1/(1 - z)/2 - 1/2 + Log[1/(1 - z)]/2 - z^2/4] - Exp[z + z^2/2!], {z, 0, nn}], z], 1] (* _Geoffrey Critzer_, Jul 23 2016 *)
%o A136284 (PARI) x='x+O('x^22); concat( [0,0], Vec( serlaplace( exp(1/(1-x)/2 - 1/2 + log(1/(1-x))/2-x^2/4) - exp(x+x^2/2!) ) ) ) \\ _Joerg Arndt_, Jul 24 2016
%Y A136284 Cf. A000085 (degree at most 1), A136281, A136282, A136283, A136285, A136286.
%K A136284 nonn
%O A136284 1,3
%A A136284 _Don Knuth_, Mar 31 2008
%E A136284 More terms from _Alois P. Heinz_, Sep 12 2008