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

1, 4, 13, 64, 721, 10624, 165313, 3672064, 154732801, 8959043584, 587435092993, 54484881424384, 9011561121239041, 2072928719458238464, 557257804202631217153, 211345500389721452314624, 138681207656726645785559041, 127174792727050845731397566464

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..18.

Formula

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

E.g.f.: Sum_{n>=0} x^(2*n+1) * exp(2^(2*n+1)*x) / (2*n+1)!.

Example

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! + ...
where
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! + ...
also
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! + ...

Prog

(PARI) {a(n) = my(A = sum(m=0, n, x^m/m! * sinh(2^m*x +x*O(x^n)) )); n!*polcoeff(A, n)}
for(n=1, 20, print1(a(n), ", "))
(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)}
for(n=1, 20, print1(a(n), ", "))

Crossrefs

Cf. A047863, A172388, A340451.

Sequence in context: A287145 A266096 A005035 * A222771 A052415 A129433

Adjacent sequences: A340449 A340450 A340451 * A340453 A340454 A340455

Keyword

nonn

Author

Paul D. Hanna, Jan 12 2021

Status

approved