A241587 Coefficients in an expansion of the trace of the log of the adjacency operator on the infinite grid Z x Z.

-1, 3, 11, 107, 759, 6039, 47403, 381051, 3088487, 25298123, 208803891, 1735293647, 14504709959, 121852053543, 1028165819931, 8709157908891, 74025669921687, 631136066733099, 5395888228066083, 46247311947563667, 397277334830158479, 3419779401039536703, 29493315403546699971

Offset

1,2

Links

Table of n, a(n) for n=1..23.

Bryan Clair, The Ihara zeta function of the infinite grid, Electron. J. Combin., 21(2) (2014), #P2.16.

Formula

a(n) = Sum_{k=0..n} n*(-3)^(n-k)*(n+k)^(-1)*binomial(n+k, 2*k)*binomial(2*k, k)^2). - Michel Marcus, Nov 23 2018

Maple

f:=n->add( n*(-3)^(n-k)*(n+k)^(-1)*binomial(n+k, 2*k)*binomial(2*k, k)^2, k=0..n);
[seq(f(n), n=1..30)];

Prog

(PARI) a(n) = sum(k=0, n, n*(-3)^(n-k)*(n+k)^(-1)*binomial(n+k, 2*k)*binomial(2*k, k)^2); \\ Michel Marcus, Nov 23 2018

Crossrefs

Sequence in context: A337734 A302927 A105413 * A183381 A136985 A131546

Adjacent sequences: A241584 A241585 A241586 * A241588 A241589 A241590

Keyword

sign

Author

N. J. A. Sloane, May 12 2014

Status

approved