cp's OEIS Frontend

A340452 E.g.f.: Sum_{n>=0} x^n * sinh(2^n*x) / n!.

%I A340452 #6 Jan 20 2021 19:00:24
%S A340452 1,4,13,64,721,10624,165313,3672064,154732801,8959043584,587435092993,
%T A340452 54484881424384,9011561121239041,2072928719458238464,
%U A340452 557257804202631217153,211345500389721452314624,138681207656726645785559041,127174792727050845731397566464
%N A340452 E.g.f.: Sum_{n>=0} x^n * sinh(2^n*x) / n!.
%C A340452 a(n) = A047863(n) - A340451(n) for n >= 0, in which A047863 gives the number of labeled graphs with 2-colored nodes when connected only to nodes of a different color.
%F A340452 E.g.f.: Sum_{n>=0} x^n * sinh(2^n*x) / n!.
%F A340452 E.g.f.: Sum_{n>=0} x^(2*n+1) * exp(2^(2*n+1)*x) / (2*n+1)!.
%e A340452 E.g.f.: A(x) = x + 4*x^2/2! + 13*x^3/3! + 64*x^4/4! + 721*x^5/5! + 10624*x^6/6! + 165313*x^7/7! + 3672064*x^8/8! + 154732801*x^9/9! + ...
%e A340452 where
%e A340452 A(x) = sinh(x) + x*sinh(2*x) + x^2*sinh(2^2*x)/2! + x^3*sinh(2^3*x)/3! + x^4*sinh(2^4*x)/4! + x^5*sinh(2^5*x)/5! + ...
%e A340452 also
%e A340452 A(x) = x*exp(2*x) + x^3*exp(2^3*x)/3! + x^5*exp(2^5*x)/5! + x^7*exp(2^7*x)/7! + x^9*exp(2^9*x)/9! + ...
%o A340452 (PARI) {a(n) = my(A = sum(m=0, n, x^m/m! * sinh(2^m*x +x*O(x^n)) )); n!*polcoeff(A, n)}
%o A340452 for(n=1, 20, print1(a(n), ", "))
%o A340452 (PARI) {a(n) = my(A = sum(m=0, n\2+1, x^(2*m+1)/(2*m+1)! * exp(2^(2*m+1)*x +x*O(x^n)) )); n!*polcoeff(A, n)}
%o A340452 for(n=1, 20, print1(a(n), ", "))
%Y A340452 Cf. A047863, A172388, A340451.
%K A340452 nonn
%O A340452 1,2
%A A340452 _Paul D. Hanna_, Jan 12 2021