A322623 E.g.f.: (1 + sinh(x)) / (1 - sinh(x)).

1, 2, 4, 14, 64, 362, 2464, 19574, 177664, 1814162, 20583424, 256891934, 3497611264, 51588733562, 819450793984, 13946142745094, 253171058212864, 4883182404118562, 99727612182790144, 2149854113300939054, 48784173816258494464, 1162353473295706049162, 29013549746780744187904, 757126891483681641073814, 20616734677807356197208064, 584789894473832421848925362

Offset: 0

Author

Paul D. Hanna, Dec 29 2018

Keywords

• nonn

Comments

Equals the antidiagonal sums of square table A322620.

a(n) = 2*A006154(n) for n >= 1.

Examples

			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 + ...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..440

Crossrefs

Cf. A322620, A012261, A006154.

Programs

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

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),", "))

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