The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A352859 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k+1) * 2^k * a(k). 2
 1, 1, 4, 25, 280, 5665, 211516, 14907673, 2021820016, 535262714881, 279317901141172, 289064917007756761, 595455410823115765768, 2446703815513439818406305, 20077597428602000393057306476, 329252263598282049972950683567705, 10794203801863458962317873561872563680 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..16. FORMULA G.f. A(x) satisfies: A(x) = 1 + x * A(2*x/(1 - x)) / (1 - x)^2. a(n) ~ c * 2^(n*(n-1)/2), where c = 8.12511731924148105991770742530352144084320407825344... - Vaclav Kotesovec, Apr 07 2022 MATHEMATICA a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k + 1] 2^k a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}] nmax = 16; A[_] = 0; Do[A[x_] = 1 + x A[2 x/(1 - x)]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] CROSSREFS Cf. A040027, A126443, A351756, A352860. Sequence in context: A320569 A058791 A216660 * A350585 A238510 A222982 Adjacent sequences: A352856 A352857 A352858 * A352860 A352861 A352862 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Apr 06 2022 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 June 17 13:47 EDT 2024. Contains 373445 sequences. (Running on oeis4.)