A322196 a(n) = [x^(n+1)*y^n/((n+1)!*n!)] (cosh(x)*cosh(y) + sinh(x) + sinh(y)) / (1 - sinh(x)*sinh(y)), for n >= 0.

1, 2, 14, 200, 4808, 174752, 8948384, 614111360, 54420050048, 6049980273152, 824598462370304, 135229597964011520, 26270107716700325888, 5966042534096492797952, 1566190258767667468673024, 470646643220470846599495680, 160520698699963165307893219328, 61671685329051568727390505009152, 26512964135663506964369113425772544, 12678129819059978095225581054619811840

Offset: 0

Author

Paul D. Hanna, Dec 29 2018

Keywords

• nonn

Comments

a(n) = A322190(n+1,n) for n >= 0.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..245

Crossrefs

Cf. A322190, A322195.

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+1, n), ", "))

Formula

a(n) ~ c * n^(2*n + 3/2) / (exp(2*n) * (log(1+sqrt(2)))^(2*n)), where c = 10.51378195853429294422318592930043390... - Vaclav Kotesovec, Dec 31 2018