The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A131764 Inverse Euler transform of central binomial coefficients A000984. 1
 1, 2, 3, 10, 30, 102, 335, 1170, 4080, 14560, 52377, 190650, 698870, 2581110, 9586395, 35791358, 134215680, 505290270, 1908866960, 7233629130, 27487764474, 104715392730, 399822314775, 1529755308210, 5864061663920, 22517998136832, 86607683851185, 333599972392960, 1286742745883790, 4969489243995030, 19215358392200893, 74382032555280450, 288230376084602880 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This is the sequence of dimensions of a free Lie algebra on some specific set of generators. LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 N. J. A. Sloane, Transforms FORMULA a(n) = (1/n) * Sum_{d|n} moebius(n/d)*2^(2*d-1) for n > 0, a(0) = 1. a(n) ~ 2^(2*n-1) / n. - Vaclav Kotesovec, Oct 09 2019 EXAMPLE 2*x + 3*x^2 + 10*x^3 + 30*x^4 + 102*x^5 + 335*x^6 + 1170*x^7 + 4080*x^8 + ... (1-x)^(-2)*(1-x^2)^(-3)*(1-x^3)^(-10)*(1-x^4)^(-30)*(1-x^5)^(-102) = 1 + 2*x + 6*x^2 + 20*x^3 + 70*x^4 + 252*x^5 + ... . MATHEMATICA a[n_] := (1/n)*DivisorSum[n, MoebiusMu[n/#]*2^(2*#-1)&]; Table[a[n], {n, 1, 32}] (* Jean-François Alcover, Feb 20 2017 *) PROG (MuPAD) a(n):=proc(n) begin 1/n*_plus(moebius(n/d)*2^(2*d-1)\$d in divisors(n)) end; (PARI) a(n)=sumdiv(n, d, 1/n*moebius(n/d)*2^(d*2-1)); /* Joerg Arndt, Jul 06 2011 */ (PARI) {a(n) = local(A); if( n<1, 0, A = sqrt(1 - 4*x + x * O(x^n)); for( k=1, n-1, A *= (1 - x^k + x * O(x^n))^ polcoeff( A, k)); -polcoeff( A, n))} /* Michael Somos, Apr 01 2012 */ CROSSREFS Cf. A022553, A000984, A000108. Sequence in context: A319671 A338593 A270363 * A066706 A209003 A080022 Adjacent sequences:  A131761 A131762 A131763 * A131765 A131766 A131767 KEYWORD nonn AUTHOR F. Chapoton, Oct 04 2007 EXTENSIONS More explicit definition from Michael Somos, Apr 01 2012. - N. J. A. Sloane, Feb 20 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 19 15:03 EDT 2021. Contains 345141 sequences. (Running on oeis4.)