A108557 Row sums of triangle A108556, in which row n equals the inverse binomial transform of the crystal ball sequence for D_n lattice.

1, 3, 9, 63, 433, 2823, 17657, 107439, 642529, 3802167, 22357097, 130970271, 765564049, 4469342439, 26073165401, 152043343119, 886424978881, 5167271805207, 30119654732489, 175558462395135, 1023255914549617

Offset

0,2

Comments

Limit a(n+1)/a(n) = 3+sqrt(8) = 5.82842712...

Links

Table of n, a(n) for n=0..20.

Formula

G.f.: (1-9*x+19*x^2+33*x^3-80*x^4+12*x^5)/(1-12*x+46*x^2-60*x^3+9*x^4).

Prog

(PARI) a(n)=local(A=vector(n+1, r, vector(n+1, c, if(r-1==0 || c-1==0, 1, if(r-1==1, 2*c-1, sum(j=0, c-1, binomial(r+c-j-2, c-j-1)*(binomial(2*r-2, 2*j)-2*(r-1)*binomial(r-3, j-1)))))))); sum(k=0, n, polcoeff(subst(Ser(A[n+1]), x, x/(1+x))/(1+x), k))

Crossrefs

Cf. A108553, A108556.

Sequence in context: A064703 A085435 A121696 * A109285 A245165 A091760

Adjacent sequences: A108554 A108555 A108556 * A108558 A108559 A108560

Keyword

nonn,easy

Author

Paul D. Hanna, Jun 10 2005

Status

approved