This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A056045 a(n) = Sum_{k|n} binomial(n,k). 22
 1, 3, 4, 11, 6, 42, 8, 107, 94, 308, 12, 1718, 14, 3538, 3474, 14827, 18, 68172, 20, 205316, 117632, 705686, 24, 3587174, 53156, 10400952, 4689778, 41321522, 30, 185903342, 32, 611635179, 193542210, 2333606816, 7049188, 10422970784, 38 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..3329 (terms 1..500 from T. D. Noe) Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1. FORMULA L.g.f.: A(x) = Sum_{n>=1} log( G(x^n,n) ) where G(x,n) = 1 + x*G(x,n)^n. L.g.f. A(x) satisfies: exp(A(x)) = g.f. of A110448. - Paul D. Hanna, Nov 10 2007 a(n) = Sum_{k=1..A000005(n)} A007318(n, A027750(k)). - Reinhard Zumkeller, Aug 13 2013 EXAMPLE A(x) = log(1/(1-x) * G(x^2,2) * G(x^3,3) * G(x^4,4) * ...) where the functions G(x,n) are g.f.s of well-known sequences: G(x,2) = g.f. of A000108 = 1 + x*G(x,2)^2; G(x,3) = g.f. of A001764 = 1 + x*G(x,3)^3; G(x,4) = g.f. of A002293 = 1 + x*G(x,4)^4; etc. MATHEMATICA f[n_] := Sum[ Binomial[n, d], {d, Divisors@ n}]; Array[f, 37] (* Robert G. Wilson v, Apr 23 2005 *) Total[Binomial[#, Divisors[#]]]&/@Range[40] (* Harvey P. Dale, Dec 08 2018 *) PROG (PARI) {a(n)=n*polcoeff(sum(m=1, n, log(1/x*serreverse(x/(1+x^m +x*O(x^n))))), n)} /* Paul D. Hanna, Nov 10 2007 */ (PARI) {a(n)=sumdiv(n, d, binomial(n, d))} /* Paul D. Hanna, Nov 10 2007 */ (Haskell) a056045 n = sum \$ map (a007318 n) \$ a027750_row n -- Reinhard Zumkeller, Aug 13 2013 CROSSREFS Cf. A110448 (exp(A(x)); A000108 (Catalan numbers), A001764, A002293, A174462. Sequence in context: A197953 A198299 A175317 * A220848 A232891 A096223 Adjacent sequences:  A056042 A056043 A056044 * A056046 A056047 A056048 KEYWORD nice,nonn AUTHOR Labos Elemer, Jul 25 2000 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 October 14 17:43 EDT 2019. Contains 328022 sequences. (Running on oeis4.)