cp's OEIS Frontend

A322625 a(n) = [x^(n+1)*y^n/(2*n+1)!] (cosh(x)*cosh(y) + sinh(x) + sinh(y)) / (1 - sinh(x)*sinh(y)), for n >= 0.

%I A322625 #5 Nov 09 2023 15:34:20
%S A322625 1,6,140,7000,605808,80735424,15355426944,3951806601600,
%T A322625 1322951416666880,558885077673235456,290849071253404145664,
%U A322625 182840964355984767938560,136612441159156704715366400,119668670961667681489160601600,121471774394099416962618586890240,141448233929575736228827518568857600,187296050462489978166693915859822510080
%N A322625 a(n) = [x^(n+1)*y^n/(2*n+1)!] (cosh(x)*cosh(y) + sinh(x) + sinh(y)) / (1 - sinh(x)*sinh(y)), for n >= 0.
%C A322625 a(n) = A322620(n+1, n) for n >= 0.
%C A322625 a(n) = binomial(2*n+1,n) * A322196(n) for n >= 0.
%o A322625 (PARI) {A322620(n, k) = my(X=x+x*O(x^n), Y=y+y*O(y^k));
%o A322625 C = cosh(X)*cosh(Y)/(1 - sinh(X)*sinh(Y));
%o A322625 S = (sinh(X) + sinh(Y))/(1 - sinh(X)*sinh(Y));
%o A322625 (n+k)!*polcoeff(polcoeff(C + S, n, x), k, y)}
%o A322625 for(n=0, 20, print1( A322620(n+1, n), ", "))
%Y A322625 Cf. A322620, A322196.
%K A322625 nonn
%O A322625 0,2
%A A322625 _Paul D. Hanna_, Jan 01 2019