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 A322195 a(n) = [x^n*y^n/n!^2] (cosh(x)*cosh(y) + sinh(x) + sinh(y)) / (1 - sinh(x)*sinh(y)), for n >= 0. 5

%I

%S 1,1,5,52,977,29056,1257125,74628352,5823720257,578189787136,

%T 71175865436645,10640402473418752,1898906773603283537,

%U 398777106584112726016,97349216334148411738565,27336588856134172778954752,8749733524560004884480322817,3166642491794673645738520477696,1286690426658870521915733780962885,583275073512315366760585608772452352,293315345943354969193393028030640310097

%N a(n) = [x^n*y^n/n!^2] (cosh(x)*cosh(y) + sinh(x) + sinh(y)) / (1 - sinh(x)*sinh(y)), for n >= 0.

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

%C a(n) = A322624(n) / binomial(2*n,n) for n >= 0.

%H Vaclav Kotesovec, <a href="/A322195/b322195.txt">Table of n, a(n) for n = 0..246</a> (terms 0..100 from Paul D. Hanna)

%F a(n) ~ c * n^(2*n + 1/2) / (exp(2*n) * (log(1+sqrt(2)))^(2*n)), where c = 9.2665697179347261408645686858011097... - _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,n),", "))

%Y Cf. A322190, A322624.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Dec 19 2018

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Last modified March 22 22:02 EDT 2023. Contains 361434 sequences. (Running on oeis4.)