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A322624 a(n) = [x^n*y^n/(2*n)!] = (cosh(x)*cosh(y) + sinh(x) + sinh(y)) / (1 - sinh(x)*sinh(y)), for n >= 0.

%I A322624 #11 Jan 01 2019 10:00:47
%S A322624 1,2,30,1040,68390,7322112,1161583500,256124504064,74951279707590,
%T A322624 28111587450552320,13150168194612783620,7506080397628737060864,
%U A322624 5134940145279960796279772,4147521174738722818202009600,3905319571990498174351316679000,4240383868623169668722969322455040,5259293239338602314365337386168258630,7389696615368349382565487880348756869120
%N A322624 a(n) = [x^n*y^n/(2*n)!] = (cosh(x)*cosh(y) + sinh(x) + sinh(y)) / (1 - sinh(x)*sinh(y)), for n >= 0.
%C A322624 a(n) = A322620(n,n) for n >= 0.
%C A322624 a(n) = A322621(n,n) for n >= 0.
%C A322624 a(n) = binomial(2*n,n) * A322195(n) for n >= 0.
%H A322624 Paul D. Hanna, <a href="/A322624/b322624.txt">Table of n, a(n) for n = 0..100</a>
%o A322624 (PARI) {A322620(n, k) = my(X=x+x*O(x^n), Y=y+y*O(y^k));
%o A322624 C = cosh(X)*cosh(Y)/(1 - sinh(X)*sinh(Y));
%o A322624 S = (sinh(X) + sinh(Y))/(1 - sinh(X)*sinh(Y));
%o A322624 (n+k)!*polcoeff(polcoeff( C + S, n, x), k, y)}
%o A322624 for(n=0,20, print1( A322620(n,n),", "))
%Y A322624 Cf. A322620, A322621, A322195.
%K A322624 nonn
%O A322624 0,2
%A A322624 _Paul D. Hanna_, Dec 29 2018