OFFSET
0,3
COMMENTS
Diagonal sums of A110519.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..925
FORMULA
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.
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
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 24 2005
STATUS
approved