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.
%I A055330 #26 Apr 19 2025 19:37:10
%S A055330 3,26,116,387,1068,2587,5678,11540,22034,39957,69366,116009,187823,
%T A055330 295574,453582,680625,1000952,1445516,2053343,2873165,3965216,5403347,
%U A055330 7277330,9695538,12787847,16708973,21642067,27802808,35443793,44859494,56391551,70434706
%N A055330 Number of rooted identity trees with n nodes and 5 leaves.
%H A055330 Andrew Howroyd, <a href="/A055330/b055330.txt">Table of n, a(n) for n = 10..1000</a>
%H A055330 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%H A055330 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-3,7,-3,0,1,0,-3,0,3,0,-1,0,3,-7,3,4,-4,1).
%F A055330 G.f.: x^10*(3 +14*x +24*x^2 +36*x^3 +41*x^4 +38*x^5 +29*x^6 +16*x^7 +6*x^8 +3*x^9)/((1-x)^9*(1+x)^3*(1+x^2)*(1+x+x^2)*(1+x+x^2+x^3+x^4)). - _Colin Barker_, Nov 07 2012
%F A055330 a(n) = (1/(8*10!))*(5303207 -25330590*n +28099260*n^2 -18286800*n^3 +7777980*n^4 -1990044*n^5 +286440*n^6 -21240*n^7 +630*n^8) -(-1)^n*(89 - 34*n +4*n^2)/2048 -(3/64)*(-1)^binomial(n+1,2) -A061347(n+1)/81 +A257145(n+2)/25. - _G. C. Greubel_, Nov 09 2023
%t A055330 Drop[CoefficientList[Series[x^10*(3+14*x+24*x^2+36*x^3+41*x^4+38*x^5+29*x^6 +16*x^7+6*x^8+3*x^9)/((1-x)^3*Product[1-x^j, {j,5}]), {x,0,40}], x], 10] (* _G. C. Greubel_, Nov 09 2023 *)
%o A055330 (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( x^10*(3 + 14*x+24*x^2+36*x^3+41*x^4+38*x^5+29*x^6+16*x^7+6*x^8+3*x^9)/((1-x)^3*(&*[1-x^j: j in [1..5]])) )); // _G. C. Greubel_, Nov 09 2023
%o A055330 (SageMath)
%o A055330 def p(x): return 3 +14*x +24*x^2 +36*x^3 +41*x^4 +38*x^5 +29*x^6 +16*x^7 +6*x^8 +3*x^9
%o A055330 def A055330_list(prec):
%o A055330 P.<x> = PowerSeriesRing(ZZ, prec)
%o A055330 return P( x^10*p(x)/((1-x)^3*product(1-x^j for j in range(1,6))) ).list()
%o A055330 a=A055330_list(50); a[10:] # _G. C. Greubel_, Nov 09 2023
%Y A055330 Column 5 of A055327.
%Y A055330 Cf. A061347, A257145.
%K A055330 nonn,easy
%O A055330 10,1
%A A055330 _Christian G. Bower_, May 12 2000