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 A055278 #25 Apr 16 2022 03:14:03
%S A055278 1,3,8,18,35,62,103,161,241,348,487,664,886,1159,1491,1890,2364,2922,
%T A055278 3574,4329,5198,6192,7322,8600,10039,11651,13450,15450,17665,20110,
%U A055278 22801,25753,28983,32508,36345,40512,45028,49911,55181,60858,66962,73514,80536
%N A055278 Number of rooted trees with n nodes and 3 leaves.
%H A055278 Georg Fischer, <a href="/A055278/b055278.txt">Table of n, a(n) for n = 4..200</a>
%H A055278 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%H A055278 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-1,0,1,2,-3,1).
%F A055278 G.f.: x^4*(x^3+x^2+1)/((1-x^2)*(1-x^3)*(1-x)^3) (conjectured). - _Ralf Stephan_, Mar 07 2004
%F A055278 a(n) = A055364(4 - n) for all n in Z. - _Michael Somos_, Jun 29 2015
%e A055278 G.f. = x^4 + 3*x^5 + 8*x^6 + 18*x^7 + 35*x^8 + 62*x^9 + 103*x^10 + ...
%t A055278 a[ n_] := Quotient[ 3 n^4 - 20 n^3 + 54 n^2 - 60 n + 32, 144];
%o A055278 (PARI) {a(n) = (3*n^4 - 20*n^3 + 54*n^2 - 60*n + 32) \ 144}; /* _Michael Somos_, Jun 29 2015 */
%o A055278 (PARI) {a(n) = if( n<0, n = -1-n; polcoeff( (1 + x + x^3) / ((1 - x)^3 * (1 - x^2) * (1 - x^3)) + x * O(x^n), n), polcoeff( x^4 * (1 + x^2 + x^3) / ((1 - x)^3 * (1 - x^2) * (1 - x^3)) + x * O(x^n), n))}; /* _Michael Somos_, Jun 29 2015 */
%Y A055278 Column 3 of A055277.
%Y A055278 Cf. A055364.
%K A055278 nonn,easy
%O A055278 4,2
%A A055278 _Christian G. Bower_, May 09 2000