A322197 Antidiagonal sums of square table A322190.

1, 2, 3, 6, 15, 46, 168, 710, 3405, 18270, 108438, 705334, 4989075, 38126414, 313034088, 2748039078, 25685633625, 254672239678, 2669718010218, 29502715813142, 342784073066655, 4177349457737262, 53279132429530428, 709785147883342726, 9858698782067445765, 142530638751865262366, 2141519206261256136318, 33391802751245681847030, 539616796036523449056555, 9026558167976152019922190

Offset

0,2

Comments

Table A322190 gives the coefficients of x^n*y^k/(n!*k!) in (cosh(x)*cosh(y) + sinh(x) + sinh(y)) / (1 - sinh(x)*sinh(y)).

Links

Paul D. Hanna, Table of n, a(n) for n = 0..150

Formula

a(n) ~ Pi * n^(n+1) / (2^(n - 3/4) * exp(n) * (log(1+sqrt(2)))^(n + 3/2)). - Vaclav Kotesovec, Dec 30 2018

Mathematica

nmax = 30;
t[n_, k_] := SeriesCoefficient[(Cosh[x] Cosh[y] + Sinh[x] + Sinh[y])/(1 - Sinh[x] Sinh[y]), {x, 0, n}, {y, 0, k}] n! k!;
a[n_] := Sum[t[n - k, k], {k, 0, n}];
Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Dec 29 2018 *)

Crossrefs

Cf. A244920.

Sequence in context: A110181 A141351 A088793 * A368954 A216144 A121688

Adjacent sequences: A322194 A322195 A322196 * A322198 A322199 A322200

Keyword

nonn

Author

Paul D. Hanna, Dec 20 2018

Status

approved