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A104979
Semidiagonal sums of triangle A104978: a(n) = Sum_{k=0..[n/2]} A104978(n-k,n-2*k).
7
1, 1, 4, 17, 85, 459, 2614, 15454, 93947, 583568, 3687761, 23633072, 153227250, 1003281314, 6624658716, 44062205158, 294938814921, 1985330061570, 13430612284606, 91262392343333, 622624395706714, 4263163419492661
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..floor(n/2)} A104978(n-k, n-2*k).
a(n) = Sum_{k=0..floor(n/2)} binomial(3*n-4*k, 3*n-5*k)*binomial(3*n-5*k, n-2*k)/(2*n-3*k+1).
G.f. satisfies: A(x) = 1 + x*A(x)^3 + x^2*A(x)^2. - Paul D. Hanna, May 27 2010
MATHEMATICA
Table[Sum[Binomial[3*n-4*k, 3*n-5*k]*Binomial[3*n-5*k, n-2*k]/(2*n-3*k+1), {k, 0, n/2}], {n, 0, 30}] (* G. C. Greubel, Jun 08 2021 *)
PROG
(PARI) {a(n)=sum(k=0, n\2, binomial(3*n-4*k, 3*n-5*k)*binomial(3*n-5*k, n-2*k)/(2*n-3*k+1))}
(Magma)
A104979:= func< n | (&+[Binomial(3*n-4*k, 3*n-5*k)*Binomial(3*n-5*k, n-2*k)/(2*n-3*k+1): k in [0..Floor(n/2)]]) >;
[A104979(n): n in [0..30]]; // G. C. Greubel, Jun 08 2021
(Sage)
def A104979(n): return sum( binomial(3*n-4*k, 3*n-5*k)*binomial(3*n-5*k, n-2*k)/(2*n-3*k+1) for k in (0..n//2) )
[A104979(n) for n in (0..30)] # G. C. Greubel, Jun 08 2021
CROSSREFS
Cf. A104978.
Sequence in context: A093904 A093344 A087316 * A081052 A020074 A163071
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 30 2005
STATUS
approved