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

%I A322623 #15 Dec 06 2019 21:45:12
%S A322623 1,2,4,14,64,362,2464,19574,177664,1814162,20583424,256891934,
%T A322623 3497611264,51588733562,819450793984,13946142745094,253171058212864,
%U A322623 4883182404118562,99727612182790144,2149854113300939054,48784173816258494464,1162353473295706049162,29013549746780744187904,757126891483681641073814,20616734677807356197208064,584789894473832421848925362
%N A322623 E.g.f.: (1 + sinh(x)) / (1 - sinh(x)).
%C A322623 Equals the antidiagonal sums of square table A322620.
%C A322623 a(n) = 2*A006154(n) for n >= 1.
%H A322623 Robert Israel, <a href="/A322623/b322623.txt">Table of n, a(n) for n = 0..440</a>
%F A322623 a(n) = Sum_{k=0..n} A322620(n-k,k), for n >= 0.
%F A322623 a(n) ~ sqrt(2)*n!/log(1+sqrt(2))^(n+1). - _Robert Israel_, Dec 31 2018
%e A322623 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! + ...
%e A322623 where
%e A322623 A(x) = 1 + 2*sinh(x) + 2*sinh(x)^2 + 2*sinh(x)^3 + 2*sinh(x)^4 + ...
%p A322623 S:= series((1+sinh(x))/(1-sinh(x)),x,51):
%p A322623 seq(coeff(S,x,j)*j!,j=0..50);  #  _Robert Israel_, Dec 31 2018
%o A322623 (PARI) {a(n) = my(X = x +x*O(x^n)); n! * polcoeff( (1 + sinh(X)) / (1 - sinh(X)),n)}
%o A322623 for(n=0,30, print1(a(n),", "))
%Y A322623 Cf. A322620, A012261, A006154.
%K A322623 nonn
%O A322623 0,2
%A A322623 _Paul D. Hanna_, Dec 29 2018