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!)
A363388 G.f. A(x) satisfies: A(x) = x + x^2 * exp( Sum_{k>=1} (-1)^(k+1) * A(x^k)^2 / (k*x^k) ). 3
1, 1, 1, 2, 5, 10, 28, 70, 190, 517, 1441, 4057, 11572, 33294, 96620, 282319, 830178, 2454384, 7292106, 21759413, 65185967, 195976025, 591097127, 1788122219, 5423917828, 16493458475, 50270190728, 153544874713, 469916030995, 1440807810639, 4425266768759, 13613578089594, 41943137192265 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
LINKS
MATHEMATICA
nmax = 33; A[_] = 0; Do[A[x_] = x + x^2 Exp[Sum[(-1)^(k + 1) A[x^k]^2/(k x^k), {k, 1, nmax}]] + O[x]^(nmax + 1)//Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
a[1] = a[2] = 1; g[n_] := g[n] = Sum[a[k] a[n - k], {k, 1, n - 1}]; a[n_] := a[n] = (1/(n - 2)) Sum[Sum[(-1)^(k/d + 1) d g[d + 1], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 33}]
PROG
(PARI) seq(n)=my(p=x+x^2+O(x^3)); for(n=1, n\2, my(m=serprec(p, x)-1); p = x + x^2*exp(-sum(k=1, m, (-1)^k*subst(p + O(x^(m\k+1)), x, x^k)^2/(x^k*k)))); Vec(p + O(x*x^n)) \\ Andrew Howroyd, May 30 2023
CROSSREFS
Sequence in context: A324838 A370316 A257889 * A287963 A006401 A283460
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 30 2023
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 3 16:49 EST 2024. Contains 370512 sequences. (Running on oeis4.)