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!)
 A357718 Expansion of e.g.f. cos( sqrt(3) * log(1+x) ). 2
 1, 0, -3, 9, -24, 60, -84, -756, 13104, -157248, 1795248, -20900880, 254007936, -3250473408, 43922668608, -626830626240, 9437477107968, -149644407564288, 2493958878657792, -43592393744250624, 797394015216175104, -15230735270523601920 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..21. Eric Weisstein's World of Mathematics, Pochhammer Symbol. FORMULA a(n) = Sum_{k=0..floor(n/2)} (-3)^k * Stirling1(n,2*k). a(n) = (-1)^n * ( (sqrt(3) * i)_n + (-sqrt(3) * i)_n )/2, where (x)_n is the Pochhammer symbol and i is the imaginary unit. a(0) = 1, a(1) = 0; a(n) = -(2*n-3) * a(n-1) - (n^2-4*n+7) * a(n-2). PROG (PARI) my(N=30, x='x+O('x^N)); apply(round, Vec(serlaplace(cos(sqrt(3)*log(1+x))))) (PARI) a(n) = sum(k=0, n\2, (-3)^k*stirling(n, 2*k, 1)); (PARI) a(n) = (-1)^n*round((prod(k=0, n-1, sqrt(3)*I+k)+prod(k=0, n-1, -sqrt(3)*I+k)))/2; (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; v[2]=0; for(i=2, n, v[i+1]=-(2*i-3)*v[i]-(i^2-4*i+7)*v[i-1]); v; CROSSREFS Column k=3 of A357720. Cf. A357703, A357726. Sequence in context: A360197 A109175 A120539 * A086796 A034330 A264685 Adjacent sequences: A357715 A357716 A357717 * A357719 A357720 A357721 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 21 19:35 EDT 2024. Contains 372738 sequences. (Running on oeis4.)