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.

1, 6, 140, 7000, 605808, 80735424, 15355426944, 3951806601600, 1322951416666880, 558885077673235456, 290849071253404145664, 182840964355984767938560, 136612441159156704715366400, 119668670961667681489160601600, 121471774394099416962618586890240, 141448233929575736228827518568857600, 187296050462489978166693915859822510080

Offset: 0

Author

Paul D. Hanna, Jan 01 2019

Keywords

• nonn

Comments

a(n) = A322620(n+1, n) for n >= 0.

a(n) = binomial(2*n+1,n) * A322196(n) for n >= 0.

Crossrefs

Cf. A322620, A322196.

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+1, n), ", "))