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
Keywords
Links
- Paul D. Hanna, Table of n, a(n) for n = 0..150
Crossrefs
Cf. A244920.
Programs
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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 *)
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
Comments