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Search: id:A056045
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| A056045 |
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Sum_{k|n} binomial(n,k). |
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+0
14
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| 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; listen)
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OFFSET
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1,2
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..500
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
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FORMULA
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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 (pauldhanna(AT)juno.com), Nov 10 2007
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EXAMPLE
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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.
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MATHEMATICA
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f[n_] := Block[{d = Divisors[n]}, Plus @@ (Binomial[n, d])]; Table[ f[n], {n, 37}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 23 2005)
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PROGRAM
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(PARI) {a(n)=n*polcoeff(sum(m=1, n, log(1/x*serreverse(x/(1+x^m +x*O(x^n))))), n)} (PARI) {a(n)=sumdiv(n, d, binomial(n, d))} - Paul D. Hanna (pauldhanna(AT)juno.com), Nov 10 2007
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CROSSREFS
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Cf. A110448 (exp(A(x)); A000108 (Catalan), A001764, A002293.
Sequence in context: A014009 A085386 A133760 this_sequence A096223 A047457 A098377
Adjacent sequences: A056042 A056043 A056044 this_sequence A056046 A056047 A056048
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KEYWORD
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nice,nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jul 25 2000
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