OFFSET
0,2
LINKS
Robert Israel, Table of n, a(n) for n = 0..440
FORMULA
a(n) = Sum_{k=0..n} A322620(n-k,k), for n >= 0.
a(n) ~ sqrt(2)*n!/log(1+sqrt(2))^(n+1). - Robert Israel, Dec 31 2018
EXAMPLE
E.g.f.: A(x) = 1 + 2*x + 4*x^2/2! + 14*x^3/3! + 64*x^4/4! + 362*x^5/5! + 2464*x^6/6! + 19574*x^7/7! + 177664*x^8/8! + 1814162*x^9/9! + ...
where
A(x) = 1 + 2*sinh(x) + 2*sinh(x)^2 + 2*sinh(x)^3 + 2*sinh(x)^4 + ...
MAPLE
S:= series((1+sinh(x))/(1-sinh(x)), x, 51):
seq(coeff(S, x, j)*j!, j=0..50); # Robert Israel, Dec 31 2018
PROG
(PARI) {a(n) = my(X = x +x*O(x^n)); n! * polcoeff( (1 + sinh(X)) / (1 - sinh(X)), n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 29 2018
STATUS
approved