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%I #6 Jan 13 2021 11:45:15
%S 1,1,3,18,217,4040,100561,3446128,192945537,18959667840,2740190273281,
%T 511238721323264,131740528383163393,56049890869822200832,
%U 38684509753685569120257,36013995749525832089671680,43327632503775311653615534081,78292881069164479582179348611072
%N E.g.f.: Sum_{n>=0} x^n * cosh(2^n*x).
%F E.g.f.: Sum_{n>=0} x^n * cosh(2^n*x).
%F E.g.f.: Sum_{n>=0} (x^(2*n)/(2*n)!) / (1 - 2^(2*n)*x).
%e E.g.f.: A(x) = 1 + x + 3*x^2/2! + 18*x^3/3! + 217*x^4/4! + 4040*x^5/5! + 100561*x^6/6! + 3446128*x^7/7! + 192945537*x^8/8! + 18959667840*x^9/9! + ...
%e where
%e A(x) = cosh(x) + x*cosh(2*x) + x^2*cosh(2^2*x) + x^3*cosh(2^3*x) + x^4*cosh(2^4*x) + x^5*cosh(2^5*x) + ...
%e also
%e A(x) = 1/(1 - x) + (x^2/2!)/(1 - 2^2*x) + (x^4/4!)/(1 - 2^4*x) + (x^6/6!)/(1 - 2^6*x) + (x^8/8!)/(1 - 2^8*x) + ...
%o (PARI) {a(n) = my(A = sum(m=0, n, x^m * cosh(2^m*x +x*O(x^n)) )); n!*polcoeff(A, n)}
%o for(n=0, 20, print1(a(n), ", "))
%o (PARI) {a(n) = my(A = sum(m=0, n\2, x^(2*m)/(2*m)! * 1/(1 - 2^(2*m)*x +x*O(x^n)) )); n!*polcoeff(A, n)}
%o for(n=0, 20, print1(a(n), ", "))
%Y Cf. A340335, A340337.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 12 2021
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