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%I #19 Sep 08 2022 08:44:52
%S 7,38,93,180,308,487,728,1043,1445,1948,2567,3318,4218,5285,6538,7997,
%T 9683,11618,13825,16328,19152,22323,25868,29815,34193,39032,44363,
%U 50218,56630,63633,71262,79553
%N a(n) = C(n+3,4) + 3*C(n+1,3) + 5*C(n-1,2) + 7*n - 15.
%H Harvey P. Dale, <a href="/A034858/b034858.txt">Table of n, a(n) for n = 2..1000</a>
%H J. Riordan, <a href="http://dx.doi.org/10.1147/rd.45.0473">Enumeration of trees by height and diameter</a>, IBM J. Res. Dev. 4 (1960), 473-478.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F G.f.: x^2*(-7-3*x+27*x^2-25*x^3+7*x^4)/(x-1)^5 . - _R. J. Mathar_, Apr 03 2017
%t Table[Binomial[n+3,4]+3Binomial[n+1,3]+5Binomial[n-1,2]+7n-15,{n,2,40}] (* _Harvey P. Dale_, Feb 04 2016 *)
%o (PARI) x='x+O('x^30); Vec(x^2*(7+3*x-27*x^2+25*x^3-7*x^4)/(1-x)^5) \\ _G. C. Greubel_, Feb 22 2018
%o (Magma) [Binomial(n+3,4)+3*Binomial(n+1,3)+5*Binomial(n-1,2)+7*n-15: n in [2..40]]; // _G. C. Greubel_, Feb 22 2018
%K nonn,easy
%O 2,1
%A _N. J. A. Sloane_
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