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

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A363387 G.f. A(x) satisfies: A(x) = x + x^2 * exp( Sum_{k>=1} A(x^k)^2 / (k*x^k) ). 3
 1, 1, 1, 3, 6, 17, 42, 120, 330, 962, 2797, 8334, 24989, 75905, 232142, 715830, 2220473, 6928411, 21723883, 68424327, 216376757, 686742855, 2186771571, 6984248840, 22368127861, 71818903891, 231132440916, 745454242656, 2409080380316, 7799945417349 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Table of n, a(n) for n=1..30. MATHEMATICA nmax = 30; A[_] = 0; Do[A[x_] = x + x^2 Exp[Sum[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[d g[d + 1], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 30}] 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, 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 Cf. A005750, A007562, A363388. Sequence in context: A121399 A212421 A238428 * A232771 A129905 A143363 Adjacent sequences: A363384 A363385 A363386 * A363388 A363389 A363390 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.

Last modified December 5 03:04 EST 2023. Contains 367567 sequences. (Running on oeis4.)