A108999 - OEIS

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

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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 * A378378 A355408 A367384

Adjacent sequences: A108996 A108997 A108998 * A109000 A109001 A109002

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 17 2005

STATUS

approved