A340909 E.g.f.: Sum_{n>=0} x^n * exp( x*exp(n*x) ) / n!.

1, 2, 4, 14, 76, 532, 4534, 46370, 559976, 7845848, 125535274, 2265367678, 45665532796, 1020237666788, 25091295382430, 675201440266298, 19774424397547216, 627298393163258800, 21464382547813040722, 789234852942189435638, 31079114556571478567396

Offset

0,2

Comments

The e.g.f. A(x) of this sequence is motivated by the following identity:

Sum_{n>=0} p^n/n! * exp(q*r^n) = Sum_{n>=0} q^n/n! * exp(p*r^n) ;

here, p = x, q = x, and r = exp(x).

Links

Table of n, a(n) for n=0..20.

Example

E.g.f.: A(x) = 1 + 2*x + 4*x^2/2! + 14*x^3/3! + 76*x^4/4! + 532*x^5/5! + 4534*x^6/6! + 46370*x^7/7! + 559976*x^8/8! + 7845848*x^9/9! + ...
where
A(x) = exp(x) + x*exp(x*exp(x)) + x^2*exp(x*exp(2*x))/2! + x^3*exp(x*exp(3*x))/3! + x^4*exp(x*exp(4*x))/4! + x^5*exp(x*exp(5*x))/5! + ...

Prog

(PARI) {a(n) = my(A=1); A = sum(m=0, n, (x^m/m!)*exp(x*exp(m*x +x*O(x^n)))); n!*polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A340332, A340335.

Sequence in context: A007712 A192815 A075098 * A052856 A093462 A302136

Adjacent sequences: A340906 A340907 A340908 * A340910 A340911 A340912

Keyword

nonn

Author

Paul D. Hanna, Jan 29 2021

Status

approved