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%I #18 Mar 05 2022 04:20:03
%S 1,4,14,39,97,212,429,804,1427,2406,3900,6094,9245,13645,19682,27791,
%T 38530,52516,70521,93390,122157,157945,202104,256090,321628,400567,
%U 495070,607445,740362,896657,1079581,1292574,1539546,1824621,2152452,2527932,2956546
%N Number of rooted trees with n nodes and 4 leaves.
%H Georg Fischer, <a href="/A055279/b055279.txt">Table of n, a(n) for n = 5..200</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F G.f.: x^5 * (1 + x + 3*x^2 + 5*x^3 + 7*x^4 + 5*x^5 + 5*x^6 + 2*x^7 + x^8) / ((1 - x)^3 * (1 - x^2)^2 * (1 - x^3) * (1 - x^4)). - _Michael Somos_, Nov 02 2014
%F a(5-n) = A055365(n). for all n in Z. - _Michael Somos_, Nov 02 2014
%F 0 = -30 + a(n) - 2*a(n+1) - a(n+2) + 3*a(n+3) + a(n+5) - 2*a(n+6) - 2*a(n+7) + a(n+8) + 3*a(n+10) - a(n+11) - 2*a(n+12) + a(n+13) for all n in Z. - _Michael Somos_, Nov 02 2014
%F a(n) ~ n^6 / 1152 as n -> infinity. - _Michael Somos_, Nov 02 2014
%e G.f. = x^5 + 4*x^6 + 14*x^7 + 39*x^8 + 97*x^9 + 212*x^10 + 429*x^11 + ...
%o (PARI) {a(n) = if( n<5, n = -1-n; polcoeff( (1 + 2*x + 5*x^2 + 5*x^3 + 7*x^4 + 5*x^5 + 3*x^6 + x^7 + x^8) / ((1 - x)^3 * (1 - x^2)^2 * (1 - x^3) * (1 - x^4)) + x * O(x^n), n), n = n-5; polcoeff( (1 + x + 3*x^2 + 5*x^3 + 7*x^4 + 5*x^5 + 5*x^6 + 2*x^7 + x^8) / ((1 - x)^3 * (1 - x^2)^2 * (1 - x^3) * (1 - x^4)) + x * O(x^n), n))}; /* _Michael Somos_, Nov 02 2014 */
%Y Column 4 of A055277.
%Y Cf. A055365.
%K nonn
%O 5,2
%A _Christian G. Bower_, May 09 2000
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