OFFSET
1,4
COMMENTS
Inverse binomial transform of A006218.
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
H. W. Gould, Binomial coefficients, the bracket function and compositions with relatively prime summands, Fib. Quart. 2, issue 4, (1964), 241-260.
FORMULA
a(n) = Sum_{j=0..n} ((-1)^(n-j)*binomial(n,j)*Sum_{k=1..j} floor(j/k)).
G.f.: Sum_{k>0} x^k/((1+x)^k-x^k).
G.f.: Sum_{k>0} tau(k)*x^k/(1+x)^k. - Vladeta Jovovic, Jun 24 2003
G.f.: Sum_{n>=1} z^n/(1-z^n) (Lambert series) where z=x/(1+x). - Joerg Arndt, Jan 30 2011
a(n) = Sum_{k=1..n} (-1)^(n-k)*binomial(n-1,k-1)*tau(k). - Ridouane Oudra, Aug 21 2021
MATHEMATICA
Table[Sum[(-1)^(n - k)*Binomial[n, k]*Sum[Floor[k/j], {j, 1, k}], {k, 0, n}], {n, 1, 50}] (* G. C. Greubel, Jul 02 2017 *)
PROG
(PARI) a(n)=sum(j=0, n, (-1)^(n-j)*binomial(n, j)*sum(k=1, j, j\k))
(PARI) a(n)=polcoeff(sum(k=1, n, x^k/((1+x)^k-x^k), x*O(x^n)), n)
CROSSREFS
KEYWORD
sign
AUTHOR
EXTENSIONS
Edited by Michael Somos, Jun 14 2003
STATUS
approved