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A108555 Antidiagonal sums of square array A108553, in which row n equals the crystal ball sequence for D_n lattice. 3
1, 2, 5, 12, 35, 116, 411, 1482, 5333, 19030, 67265, 235704, 819863, 2834600, 9752951, 33428054, 114228713, 389419114, 1325155261, 4503031332, 15285291851, 51842203804, 175719341971, 595316455842, 2016131645245, 6826076021310 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Limit a(n+1)/a(n) ~ 3.3829757679..., real root of cubic (1+x+3*x^2-x^3).

LINKS

Table of n, a(n) for n=0..25.

FORMULA

Empirical G.f.: (x^3+x^2+x-1)*(2*x^5+5*x^4-4*x^3+10*x^2-6*x+1) / ((x-1)^2*(x^2+2*x-1)^2*(x^3+x^2+3*x-1)). [Colin Barker, Nov 21 2012]

PROG

(PARI) {a(n)=if(n<0, 0, if(n==0, 1, sum(k=0, n, sum(j=0, k, binomial(n-j, k-j)* (binomial(2*(n-k), 2*j)-2*j*(n-k-j)*binomial(n-k, j)/if(n==k+1, 1, (n-k-1)))))))}

CROSSREFS

Cf. A108553, A108554.

Sequence in context: A000104 A000105 A055192 * A292169 A283799 A225798

Adjacent sequences:  A108552 A108553 A108554 * A108556 A108557 A108558

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 10 2005

STATUS

approved

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Last modified February 21 14:23 EST 2018. Contains 299414 sequences. (Running on oeis4.)