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%I #14 Nov 06 2023 04:19:39
%S 1,2,8,64,768,12068,236926,5651384,160054952,5284391984,200375581984,
%T 8620342917808,416471882713712,22400989824444576,1331457489258580672,
%U 86887134810544955072,6189888588922841477824,478992737680928902742656,40082045451011806706919808,3612470757307682016196841216,349398857659776033845292636416
%N Number of graphs on n labeled nodes with degree at most 3.
%D D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.
%H Alois P. Heinz, <a href="/A136282/b136282.txt">Table of n, a(n) for n = 1..200</a>
%F Binomial transform of A110041. - _Vladeta Jovovic_, May 20 2008
%F Recurrence: 12*(81*n^4 - 837*n^3 + 3375*n^2 - 6171*n + 4192)*a(n) = 6*(243*n^5 - 2511*n^4 + 10665*n^3 - 21969*n^2 + 19476*n - 4624)*a(n-1) + 3*(n-1)*(243*n^6 - 2997*n^5 + 15147*n^4 - 39843*n^3 + 57594*n^2 - 41832*n + 10888)*a(n-2) - 3*(n-2)*(n-1)*(405*n^5 - 3699*n^4 + 13527*n^3 - 22629*n^2 + 14048*n + 388)*a(n-3) + (n-3)*(n-2)*(n-1)*(243*n^5 - 1944*n^4 + 6777*n^3 - 9738*n^2 - 2370*n + 10732)*a(n-4) + 2*(n-4)*(n-3)*(n-2)*(n-1)*(81*n^4 - 999*n^3 + 4968*n^2 - 8646*n + 4906)*a(n-5) + (n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(243*n^5 - 2916*n^4 + 12933*n^3 - 27990*n^2 + 27978*n - 8948)*a(n-6) - (n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(81*n^4 - 513*n^3 + 891*n^2 - 357*n - 242)*a(n-7) - (n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(81*n^4 - 513*n^3 + 1350*n^2 - 1608*n + 640)*a(n-8). - _Vaclav Kotesovec_, Aug 13 2013
%F a(n) ~ 3^(n/2) * exp(sqrt(3*n) - 3*n/2 - 5/4) * n^(3*n/2) / 2^(n + 1/2) * (1 + 71/(24*sqrt(3*n))). - _Vaclav Kotesovec_, Nov 05 2023
%F a(n) / A110041(n) ~ 1 + 2/sqrt(3*n). - _Vaclav Kotesovec_, Nov 06 2023
%Y Cf. A000085 (degree at most 1), A136281-A136286.
%K nonn
%O 1,2
%A _Don Knuth_, Mar 31 2008
%E More terms from _Vladeta Jovovic_, May 20 2008
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