login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A326435 E.g.f.: exp(-4) * Sum_{n>=0} (exp(n*x) + 3)^n / n!. 5
1, 5, 69, 1496, 45771, 1840537, 92925982, 5705543791, 416015394341, 35365673566750, 3454046493504337, 382930667897753421, 47708365129614794580, 6622948820406278058625, 1016977626656613380728781, 171637260767262574245781800, 31661205827344145981298200207, 6352045190999137085697971335893 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
More generally, the following sums are equal:
(1) exp(-(p+1)*r) * Sum_{n>=0} (q^n + p)^n * r^n / n!,
(2) exp(-(p+1)*r) * Sum_{n>=0} q^(n^2) * exp(p*q^n*r) * r^n / n!,
here, q = exp(x), p = 3, r = 1.
LINKS
FORMULA
E.g.f.: exp(-4) * Sum_{n>=0} (exp(n*x) + 3)^n / n!.
E.g.f.: exp(-4) * Sum_{n>=0} exp(n^2*x) * exp( 3*exp(n*x) ) / n!.
FORMULAS FOR TERMS.
a(3*n) = 0 (mod 2), a(3*n-1) = 1 (mod 2), and a(3*n-2) = 1 (mod 2) for n > 0.
EXAMPLE
E.g.f.: A(x) = 1 + 5*x + 69*x^2/2! + 1496*x^3/3! + 45771*x^4/4! + 1840537*x^5/5! + 92925982*x^6/6! + 5705543791*x^7/7! + 416015394341*x^8/8! + 35365673566750*x^9/9! + 3454046493504337*x^10/10! + ...
such that
A(x) = exp(-4) * (1 + (exp(x) + 3) + (exp(2*x) + 3)^2/2! + (exp(3*x) + 3)^3/3! + (exp(4*x) + 3)^4/4! + (exp(5*x) + 3)^5/5! + (exp(6*x) + 3)^6/6! + ...)
also
A(x) = exp(-4) * (exp(3) + exp(x)*exp(3*exp(x)) + exp(4*x)*exp(3*exp(2*x))/2! + exp(9*x)*exp(3*exp(3*x))/3! + exp(16*x)*exp(3*exp(4*x))/4! + exp(25*x)*exp(3*exp(5*x))/5! + exp(36*x)*exp(3*exp(6*x))/6! + ...).
PROG
(PARI) /* Requires suitable precision */
\p200
Vec(round(serlaplace( exp(-4) * sum(n=0, 500, (exp(n*x +O(x^31)) + 3)^n/n! ) )))
CROSSREFS
Sequence in context: A333459 A362101 A307700 * A231294 A302543 A157038
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 11 2019
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)