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A159309 L.g.f.: Sum_{n>=1} a(n)*x^n/n = Sum_{n>=1} (1 + sigma(n)*x)^n * x^n/n. 1

%I

%S 1,3,10,35,116,606,2990,11203,65368,567558,3229942,12730946,78628616,

%T 666394746,3968286590,21143707843,160244432497,1602468019110,

%U 20852615681805,320475672814590,4102188681702086,36438823274699332

%N L.g.f.: Sum_{n>=1} a(n)*x^n/n = Sum_{n>=1} (1 + sigma(n)*x)^n * x^n/n.

%F a(n) = n * Sum_{k=0..[n/2]} C(n-k,k)*sigma(n-k)^k/(n-k) for n>=1.

%e L.g.f.: L(x) = x + 3*x^2/2 + 10*x^3/3 + 35*x^4/4 + 116*x^5/5 +...

%e L(x) = (1+x)*x + (1+3*x)^2*x^2/2 + (1+4*x)^3*x^3/3 + (1+7*x)^4*x^4/4 +...

%e exp(L(x)) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 40*x^5 + 154*x^6 +... (A159308).

%o (PARI) {a(n)=n*polcoeff(sum(m=1,n+1,(1+sigma(m)*x+x*O(x^n))^m*x^m/m),n)}

%o (PARI) {a(n)=n*sum(k=0,n\2,binomial(n-k,k)*sigma(n-k)^k/(n-k))}

%Y Cf. A159308 (exp).

%K nonn

%O 1,2

%A _Paul D. Hanna_, Apr 10 2009

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Last modified May 16 22:37 EDT 2022. Contains 353724 sequences. (Running on oeis4.)