%I #11 Dec 31 2018 08:00:31

%S 1,2,14,200,4808,174752,8948384,614111360,54420050048,6049980273152,

%T 824598462370304,135229597964011520,26270107716700325888,

%U 5966042534096492797952,1566190258767667468673024,470646643220470846599495680,160520698699963165307893219328,61671685329051568727390505009152,26512964135663506964369113425772544,12678129819059978095225581054619811840

%N a(n) = [x^(n+1)*y^n/((n+1)!*n!)] (cosh(x)*cosh(y) + sinh(x) + sinh(y)) / (1 - sinh(x)*sinh(y)), for n >= 0.

%C a(n) = A322190(n+1,n) for n >= 0.

%H Vaclav Kotesovec, <a href="/A322196/b322196.txt">Table of n, a(n) for n = 0..245</a>

%F a(n) ~ c * n^(2*n + 3/2) / (exp(2*n) * (log(1+sqrt(2)))^(2*n)), where c = 10.51378195853429294422318592930043390... - _Vaclav Kotesovec_, Dec 31 2018

%o (PARI) {A322190(n, k) = my(X=x+x*O(x^n), Y=y+y*O(y^k));

%o C = cosh(X)*cosh(Y)/(1 - sinh(X)*sinh(Y));

%o S = (sinh(X) + sinh(Y))/(1 - sinh(X)*sinh(Y));

%o n!*k!*polcoeff(polcoeff( C + S, n, x), k, y)}

%o for(n=0, 20, print1( A322190(n+1, n), ", "))

%Y Cf. A322190, A322195.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Dec 29 2018