A108627 Logarithmic g.f.: Sum_{n>=1} a(n)/n*x^n = log(G108626(x)), where G108626(x) is g.f. for A108626.

2, 6, 20, 66, 222, 750, 2536, 8578, 29018, 98166, 332092, 1123458, 3800630, 12857438, 43496400, 147147266, 497795634, 1684030566, 5697034596, 19272929986, 65199855118, 220569529934, 746181374904, 2524313509762

Offset: 1

Author

Paul D. Hanna, Jun 13 2005

Keywords

• nonn

Comments

A108626 forms the antidiagonal sums of square array A108625, in which row n equals the crystal ball sequence for A_n lattice.

Crossrefs

Cf. A108625, A108626.

Programs

PARI

a(n)=polcoeff(2*x*(1-x-x^3)/(1-4*x+2*x^2+x^4+x*O(x^n)),n)

PARI

/* Logarithm of g.f. of A108626: */ a(n)=n*polcoeff(log(sum(k=0,n,sum(j=0,k, sum(i=0,j,binomial(k-j,i)^2*binomial(k-i,j-i)))*x^k)+x*O(x^n)),n)

Formula

G.f.: A(x) = 2*x*(1 - x - x^3)/(1 - 4*x + 2*x^2 + x^4).