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

1, 3, 10, 35, 116, 606, 2990, 11203, 65368, 567558, 3229942, 12730946, 78628616, 666394746, 3968286590, 21143707843, 160244432497, 1602468019110, 20852615681805, 320475672814590, 4102188681702086, 36438823274699332

Offset

1,2

Links

Table of n, a(n) for n=1..22.

Formula

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

Example

L.g.f.: L(x) = x + 3*x^2/2 + 10*x^3/3 + 35*x^4/4 + 116*x^5/5 +...
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 +...
exp(L(x)) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 40*x^5 + 154*x^6 +... (A159308).

Prog

(PARI) {a(n)=n*polcoeff(sum(m=1, n+1, (1+sigma(m)*x+x*O(x^n))^m*x^m/m), n)}
(PARI) {a(n)=n*sum(k=0, n\2, binomial(n-k, k)*sigma(n-k)^k/(n-k))}

Crossrefs

Cf. A159308 (exp).

Sequence in context: A099907 A128735 A330050 * A112107 A187925 A372852

Adjacent sequences: A159306 A159307 A159308 * A159310 A159311 A159312

Keyword

nonn

Author

Paul D. Hanna, Apr 10 2009

Status

approved