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.

1, 1, 5, 52, 977, 29056, 1257125, 74628352, 5823720257, 578189787136, 71175865436645, 10640402473418752, 1898906773603283537, 398777106584112726016, 97349216334148411738565, 27336588856134172778954752, 8749733524560004884480322817, 3166642491794673645738520477696, 1286690426658870521915733780962885, 583275073512315366760585608772452352, 293315345943354969193393028030640310097

Offset: 0

Author

Paul D. Hanna, Dec 19 2018

Keywords

• nonn

Comments

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

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

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..246 (terms 0..100 from Paul D. Hanna)

Crossrefs

Cf. A322190, A322624.

Programs

PARI

{A322190(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( A322190(n,n),", "))

Formula

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