OFFSET
1,1
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..3000
Vaclav Kotesovec, Plot of a(n)/(n*2^n) for n = 1..10000
FORMULA
Equals the logarithmic derivative of A181410.
Conjecture: a(n) ~ c * n * 2^n, where c = Pi^2/4 = A091476. - Vaclav Kotesovec, Oct 05 2020
EXAMPLE
L.g.f.: L(x) = 4*x + 18*x^2/2 + 55*x^3/3 + 150*x^4/4 + 379*x^5/5 +...
Exponentiation yields the g.f. of A181410:
exp(L(x)) = 1 + 4*x + 17*x^2 + 65*x^3 + 234*x^4 + 804*x^5 +...
The initial terms begin:
a(1) = 1*1 + 1*3 = 4;
a(2) = 1*3 + 2*4 + 1*7 = 18;
a(3) = 1*4 + 3*7 + 3*6 + 1*12 = 55;
a(4) = 1*7 + 4*6 + 6*12 + 4*8 + 1*15 = 150; ...
MATHEMATICA
Table[Sum[Binomial[n, k] * DivisorSigma[1, n+k], {k, 0, n}], {n, 1, 30}] (* Vaclav Kotesovec, Oct 05 2020 *)
PROG
(PARI) {a(n)=sum(k=0, n, binomial(m, k)*sigma(n+k))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 19 2010
STATUS
approved