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!)
 A357725 Expansion of e.g.f. cos( sqrt(2) * (exp(x) - 1) ). 4
 1, 0, -2, -6, -10, 10, 190, 1106, 4438, 9978, -35250, -666622, -5657370, -35308182, -155215970, -128513870, 7051468022, 105057922906, 1042016038254, 8053738122466, 44608555196294, 48639210067658, -3200193654245442, -60669816166988654, -769281697485061994 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..200 Eric Weisstein's World of Mathematics, Bell Polynomial. FORMULA a(n) = Sum_{k=0..floor(n/2)} (-2)^k * Stirling2(n,2*k). a(n) = 1; a(n) = -2 * Sum_{k=0..n-1} binomial(n-1, k) * A357736(k). a(n) = ( Bell_n(sqrt(2) * i) + Bell_n(-sqrt(2) * i) )/2, where Bell_n(x) is n-th Bell polynomial and i is the imaginary unit. PROG (PARI) my(N=30, x='x+O('x^N)); apply(round, Vec(serlaplace(cos(sqrt(2)*(exp(x)-1))))) (PARI) a(n) = sum(k=0, n\2, (-2)^k*stirling(n, 2*k, 2)); (PARI) Bell_poly(n, x) = exp(-x)*suminf(k=0, k^n*x^k/k!); a(n) = round((Bell_poly(n, sqrt(2)*I)+Bell_poly(n, -sqrt(2)*I)))/2; CROSSREFS Column k=2 of A357728. Cf. A121867, A264036, A357736. Sequence in context: A054645 A337645 A225271 * A050425 A030405 A125241 Adjacent sequences: A357722 A357723 A357724 * A357726 A357727 A357728 KEYWORD sign AUTHOR Seiichi Manyama, Oct 10 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 May 25 17:00 EDT 2024. Contains 372804 sequences. (Running on oeis4.)