A299437 - OEIS

%I #11 Feb 17 2018 12:28:35

%S 1,1,2,3,7,9,27,33,73,100,203,269,987,1163,2283,3234,6706,8812,21455,

%T 27211,55718,76055,147048,196483,533149,659549,1262531,1759301,

%U 3462333,4593487,10261739,13213278,25944342,35397849,66694451,89412873,209286231,266115126,499426529,689936238,1311854563,1750578063,3676669661,4787587399,9114353938,12427479022,22925519170

%N G.f.: exp( Sum_{n>=1} A020696(n)/2 * x^n/n ), where A020696(n) = Product_{d|n} (d + 1).

%C Self-convolution equals A299436.

%H Paul D. Hanna, <a href="/A299437/b299437.txt">Table of n, a(n) for n = 0..1000</a>

%e G.f.: A(x) = 1 + x + 2*x^2 + 3*x^3 + 7*x^4 + 9*x^5 + 27*x^6 + 33*x^7 + 73*x^8 + 100*x^9 + 203*x^10 + 269*x^11 + 987*x^12 + 1163*x^13 + 2283*x^14 + ...

%e such that

%e log(A(x)) = x + 3*x^2/2 + 4*x^3/3 + 15*x^4/4 + 6*x^5/5 + 84*x^6/6 + 8*x^7/7 + 135*x^8/8 + 40*x^9/9 + 198*x^10/10 + 12*x^11/11 + 5460*x^12/12 + 14*x^13/13 + 360*x^14/14 + 384*x^15/15 + ... + A020696(n)/2*x^n/n + ...

%o (PARI) A020696(n) = {d = divisors(n); return (prod(i=1, #d, d[i]+1)); } \\ after _Michel Marcus_

%o {a(n) = my(A = exp( sum(m=1,n, A020696(m)/2*x^m/m ) +x*O(x^n) )); polcoeff(A,n)}

%o for(n=0,40,print1(a(n),", "))

%Y Cf. A299436 (A(x)^2), A020696.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Feb 12 2018