# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a007831 Showing 1-1 of 1 %I A007831 #21 Sep 08 2022 08:44:35 %S A007831 1,0,1,1,16,61,806,6329,89272,1082281,17596162,284074165,5407229972, %T A007831 107539072733,2380274168806,55833426732529,1418006883852784, %U A007831 38195636967960913,1097755724834189834,33345176998235584301,1071124330593423824908,36203857373308709200645 %N A007831 Number of edge-labeled series-reduced trees with n nodes. %H A007831 G. C. Greubel, Table of n, a(n) for n = 1..400 %H A007831 P. J. Cameron, Counting two-graphs related to trees, Elec. J. Combin., Vol. 2, #R4. %H A007831 Index entries for sequences related to trees %F A007831 a(n) = A005512(n+1) / (n+1) for n >= 2. - _Sean A. Irvine_, Feb 03 2018 %F A007831 E.g.f.: 1/(2*x) + (x-1)/2 - ((1+x)/(2*x))*(1 + LambertW(-x/(1+x)))^2. - _G. C. Greubel_, Mar 08 2020 %p A007831 seq( `if`(n=1, 1, (n-1)!*add((-1)^k*binomial(n+1, k)*(n-k+1)^(n-k-1)/( (n+1)*(n-k-1)!), k = 0..n-1)), n=1..20); # _G. C. Greubel_, Mar 08 2020 %t A007831 Table[If[n==1, 1, (n-1)!*Sum[(-1)^k*Binomial[n+1,k]*(n-k+1)^(n-k-1)/((n+1)*(n - k-1)!), {k,0,n-1}]], {n, 20}] (* _G. C. Greubel_, Mar 08 2020 *) %o A007831 (PARI) a(n) = if(n==1, 1, (n-1)!*sum(k=0, n-1, (-1)^k*binomial(n+1,k)*(n-k+1 )^(n-k-1)/( (n+1)*(n-k-1)!))); \\ _G. C. Greubel_, Mar 08 2020 %o A007831 (Magma) [1] cat [Factorial(n-1)*(&+[(-1)^k*Binomial(n+1,k)*(n-k+1)^(n-k-1)/((n+1)*Factorial(n-k-1)): k in [0..n-1]]): n in [2..20]] // _G. C. Greubel_, Mar 08 2020 %o A007831 (Sage) [1]+[factorial(n-1)*sum((-1)^k*binomial(n+1,k)*(n-k+1)^(n-k-1)/( (n+1)*factorial(n-k-1)) for k in (0..n-1)) for n in (2..20)] # _G. C. Greubel_, Mar 08 2020 %Y A007831 Cf. A005512. %K A007831 nonn %O A007831 1,5 %A A007831 _Peter J. Cameron_ # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE