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A110521 Expansion of 1/(1 - (x + x^2)c(3x)), c(x) the g.f. of A000108. 2

%I

%S 1,1,5,30,224,1871,16771,157668,1533970,15314626,156008660,1615147014,

%T 16944659846,179746651907,1924700759635,20776060271760,

%U 225838715259574,2469974866825150,27160344857205806,300101157823582668

%N Expansion of 1/(1 - (x + x^2)c(3x)), c(x) the g.f. of A000108.

%C Diagonal sums of A110519.

%H G. C. Greubel, <a href="/A110521/b110521.txt">Table of n, a(n) for n = 0..925</a>

%F a(0) = 1, a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..(n-k)} j*C(2*n-2*k-j-1, n-k-j)*C(j, k)*3^(n-k-j)/(n-k), n > 0.

%F Conjecture: 2*n*a(n) + 2*(16-11n)*a(n-1) + 2*(42-11n)*a(n-2) + (32-21n)*a(n-3) + 5*(20-7n)*a(n-4) + 6*(7-2n)*a(n-5) = 0. - _R. J. Mathar_, Dec 10 2011

%t T[0, 0] := 1; T[n_, k_] := Sum[j*3^(n - k - j)*Binomial[2*n - 2*k - j - 1, n - k - j]*Binomial[j, k]/(n - k), {j, 0, n - k}]; Table[Sum[T[n, k], {k, 0, Floor[n/2]}], {n, 0, 50}] (* _G. C. Greubel_, Aug 29 2017 *)

%o (PARI) concat([1], for(n=1,20, print1(sum(k=0, n\2, sum(j=0, n-k, j*binomial(2*n-2*k-j-1, n-k-j)*binomial(j, k)*3^(n-k-j)/(n-k))), ", "))) \\ _G. C. Greubel_, Aug 29 2017

%K easy,nonn

%O 0,3

%A _Paul Barry_, Jul 24 2005

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Last modified February 17 15:19 EST 2019. Contains 320220 sequences. (Running on oeis4.)