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A322197 Antidiagonal sums of square table A322190. 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Dec 29 2018 *)

CROSSREFS

Cf. A244920.

Sequence in context: A110181 A141351 A088793 * A216144 A121688 A082094

Adjacent sequences:  A322194 A322195 A322196 * A322198 A322199 A322200

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 20 2018

STATUS

approved

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Last modified July 11 01:51 EDT 2020. Contains 335600 sequences. (Running on oeis4.)