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A322197 Antidiagonal sums of square table A322190. 3

%I

%S 1,2,3,6,15,46,168,710,3405,18270,108438,705334,4989075,38126414,

%T 313034088,2748039078,25685633625,254672239678,2669718010218,

%U 29502715813142,342784073066655,4177349457737262,53279132429530428,709785147883342726,9858698782067445765,142530638751865262366,2141519206261256136318,33391802751245681847030,539616796036523449056555,9026558167976152019922190

%N Antidiagonal sums of square table A322190.

%C 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)).

%H Paul D. Hanna, <a href="/A322197/b322197.txt">Table of n, a(n) for n = 0..150</a>

%F a(n) ~ Pi * n^(n+1) / (2^(n - 3/4) * exp(n) * (log(1+sqrt(2)))^(n + 3/2)). - _Vaclav Kotesovec_, Dec 30 2018

%t nmax = 30;

%t 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!;

%t a[n_] := Sum[t[n - k, k], {k, 0, n}];

%t Table[a[n], {n, 0, nmax}] (* _Jean-Fran├žois Alcover_, Dec 29 2018 *)

%Y Cf. A244920.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Dec 20 2018

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Last modified May 17 05:13 EDT 2021. Contains 343965 sequences. (Running on oeis4.)