A108999 Main diagonal of square array A108998, in which row n equals the coordination sequence of B_n lattice.

1, 2, 16, 170, 1856, 20082, 214864, 2282394, 24165120, 255708578, 2708805776, 28752157898, 305908697152, 3262741154194, 34882914424528, 373781033269306, 4013444615232512, 43174945822078530, 465247083731404048

Offset

0,2

Comments

Compare to diagonal A108554 of square array A108553, in which row n equals the crystal ball sequence for D_n lattice.

Links

Muniru A Asiru, Table of n, a(n) for n = 0..900

Formula

a(n) = Sum_{j=0..n} C(2*n-j-1, n-j)*( C(2*n+1, 2*j) - 2*n*C(n-1, j-1) ).

Mathematica

a[n_]:= Sum[Binomial[2*n-j-1, n-j]*(Binomial[2*n+1, 2*j] - 2*n*Binomial[n-1, j-1]), {j, 0, n}]; Array[a, 20, 0] (* Stefano Spezia, Nov 21 2018 *)

Prog

(PARI) {a(n)=sum(j=0, n, binomial(2*n-j-1, n-j)*(binomial(2*n+1, 2*j)-2*n*binomial(n-1, j-1)))}
(GAP) List([0..20], n->Sum([0..n], j->Binomial(2*n-j-1, n-j)*(Binomial(2*n+1, 2*j)-2*n*Binomial(n-1, j-1)))); # Muniru A Asiru, Nov 21 2018

Crossrefs

Cf. A108998, A109000, A109001.

Sequence in context: A219446 A215702 A155659 * A355408 A138014 A206988

Adjacent sequences: A108996 A108997 A108998 * A109000 A109001 A109002

Keyword

nonn

Author

Paul D. Hanna, Jun 17 2005

Status

approved