OFFSET
1,2
COMMENTS
Logarithmic derivative of A184512.
EXAMPLE
L.g.f.: L(x) = x + 5*x^2/2 + 19*x^3/3 + 89*x^4/4 + 351*x^5/5 + ...
The l.g.f. equals the series:
L(x) = x/sqrt(1-4*x) + (x^2/2)/sqrt(1-8*x^2) + (x^3/3)/sqrt(1-16*x^3) + (x^4/4)/sqrt(1-32*x^4) + (x^5/5)/sqrt(1-64*x^5) + ...
The g.f. of A184512 begins:
exp(L(x)) = 1 + x + 3*x^2 + 9*x^3 + 33*x^4 + 115*x^5 + 445*x^6 + ...
MATHEMATICA
a[n_] := DivisorSum[n, 2^((#-1)*(n/#-1)) * Binomial[2*(#-1), #-1] * # &]; Array[a, 25] (* Amiram Eldar, Aug 18 2023 *)
PROG
(PARI) {a(n)=if(n<1, 0, sumdiv(n, d, 2^((d-1)*(n/d-1))*binomial(2*(d-1), d-1)*d))}
(PARI) {a(n)=n*polcoeff(sum(m=1, n, (x^m/m)/sqrt(1-2*(2*x)^m+x*O(x^n))), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 18 2011
EXTENSIONS
a(24)-a(26) from Amiram Eldar, Aug 18 2023
STATUS
approved