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.

1, 2, 30, 1040, 68390, 7322112, 1161583500, 256124504064, 74951279707590, 28111587450552320, 13150168194612783620, 7506080397628737060864, 5134940145279960796279772, 4147521174738722818202009600, 3905319571990498174351316679000, 4240383868623169668722969322455040, 5259293239338602314365337386168258630, 7389696615368349382565487880348756869120

Offset: 0

Author

Paul D. Hanna, Dec 29 2018

Keywords

• nonn

Comments

a(n) = A322620(n,n) for n >= 0.

a(n) = A322621(n,n) for n >= 0.

a(n) = binomial(2*n,n) * A322195(n) for n >= 0.

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A322620, A322621, A322195.

Programs

PARI

{A322620(n, k) = my(X=x+x*O(x^n), Y=y+y*O(y^k));
C = cosh(X)*cosh(Y)/(1 - sinh(X)*sinh(Y));
S = (sinh(X) + sinh(Y))/(1 - sinh(X)*sinh(Y));
(n+k)!*polcoeff(polcoeff( C + S, n, x), k, y)}
for(n=0,20, print1( A322620(n,n),", "))