|
%I #12 Sep 08 2022 08:45:21
%S 2,18,108,562,2724,12660,57240,253842,1109748,4798780,20572392,
%T 87580308,370706408,1561573032,6551178288,27387484242,114146434068,
%U 474476717292,1967642119368,8142727008732,33634295542968,138696447565272
%N a(n) = (n+1)*binomial(2n+2,n+1)-3*4^n+binomial(2n,n).
%C Row sums of A112327.
%H Robert Israel, <a href="/A112328/b112328.txt">Table of n, a(n) for n = 1..1656</a>
%H F. Ruskey, <a href="https://doi.org/10.1137/0601007">Average shape of binary trees</a>, SIAM J. Alg. Disc. Meth., 1, 1980, 43-50 (Eq. (8)).
%F G.f.: 4z[2-sqrt(1-4z)]/[(1-4z)^(3/2)(1+sqrt(1-4z)]
%F 32*(2*n^2 - 9*n + 10)*a(n - 3) - 8*(2*n^2 - 14*n + 15)*a(n - 2) - 2*(2*n^2 + 3*n - 5)*a(n - 1) + n*(n - 1)*a(n) = 0. - _Robert Israel_, Sep 19 2019
%p a:=n->(n+1)*binomial(2*n+2,n+1)-3*4^n+binomial(2*n,n): seq(a(n),n=1..25);
%t a[n_]:=(n+1)*Binomial[2n+2,n+1]-3*4^n+Binomial[2n,n]; Array[a,22] (* _Stefano Spezia_, Sep 20 2019 *)
%o (PARI) a(n) = (n+1)*binomial(2*n+2,n+1)-3*4^n+binomial(2*n,n); \\ _Michel Marcus_, Sep 20 2019
%o (Magma) [(n+1)*Binomial(2*n+2,n+1)-3*4^n+Binomial(2*n,n):n in [1..22]]; // _Marius A. Burtea_, Sep 20 2019
%Y Cf. A112327.
%K nonn
%O 1,1
%A _Emeric Deutsch_, Sep 04 2005
|
