A299436 - OEIS

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

%S 1,2,5,10,24,44,109,198,423,766,1555,2730,6269,11090,22127,39246,

%T 77541,134242,270348,467004,895797,1546922,2905899,4943126,9666435,

%U 16471506,30604583,52206218,96412319,162467222,303289098,510436808,929735638,1564811464,2818065892,4700325864,8619686709,14378564170,25693238857,42876196186,76267527522,126317457712

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

%C Self-convolution of A299437.

%H Paul D. Hanna, <a href="/A299436/b299436.txt">Table of n, a(n) for n = 0..1000</a>

%e G.f.: A(x) = 1 + 2*x + 5*x^2 + 10*x^3 + 24*x^4 + 44*x^5 + 109*x^6 + 198*x^7 + 423*x^8 + 766*x^9 + 1555*x^10 + 2730*x^11 + 6269*x^12 + 11090*x^13 + ...

%e such that

%e log(A(x)) = 2*x + 6*x^2/2 + 8*x^3/3 + 30*x^4/4 + 12*x^5/5 + 168*x^6/6 + 16*x^7/7 + 270*x^8/8 + 80*x^9/9 + 396*x^10/10 + 24*x^11/11 + 10920*x^12/12 + 28*x^13/13 + 720*x^14/14 + 768*x^15/15 + ... + A020696(n)*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)*x^m/m ) +x*O(x^n) )); polcoeff(A,n)}

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

%Y Cf. A299437 (sqrt(A(x))), A020696.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 12 2018