OFFSET
2,2
REFERENCES
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 139, b(n,2).
LINKS
Robert Israel, Table of n, a(n) for n = 2..414
FORMULA
a(n) = A008296(n,2).
E.g.f.: ((1+x)*log(1+x))^2/2. - Vladeta Jovovic, Feb 20 2003
a(n) = sum(i=1, n-1, i^2*Stirling1(n-1, i)). - Benoit Cloitre, Oct 23 2004
If we define f(n,i,a)=sum(binomial(n,k)*stirling1(n-k,i)*product(-a-j,j=0..k-1),k=0..n-i), then a(n) = f(n,2,-2), for n>=2. - Milan Janjic, Dec 21 2008
a(n) = (-1)^(n)*(2*H(n-3)-3)*(n-3)! for n >= 3, where H(n) = Sum(j=1..n, 1/j) is the n-th harmonic number. - Gary Detlefs, Feb 13 2010
a(n) = 2*A081048(n-3)-3*(-1)^(n)*(n-3)! for n >= 3. - Robert Israel, Jun 28 2015
Sum_{k=1..n} a(k+1) * Stirling2(n,k) = n^2. - Vaclav Kotesovec, Sep 03 2018
Conjecture: D-finite with recurrence a(n) +(2*n-7)*a(n-1) +(n-4)^2*a(n-2)=0. - R. J. Mathar, Sep 15 2021
MAPLE
with(combinat): for n from 2 to 40 do for k from 2 to 2 do printf(`%d, `, sum(binomial(l, k)*k^(l-k)*stirling1(n, l), l=k..n)) od: od:
# Alternative:
A081048:= gfun:-rectoproc({a(0)=0, a(1)=1, a(n)=(1-2*n)*a(n-1) -(n-1)^2*a(n-2)}, a(n), remember):
1, seq(2*A081048(n-3)-3*(-1)^(n)*(n-3)!, n=3..50); # Robert Israel, Jun 29 2015
MATHEMATICA
With[{nn=30}, CoefficientList[Series[((1+x)Log[1+x])^2/2, {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Jun 04 2019 *)
CROSSREFS
KEYWORD
sign,easy
AUTHOR
N. J. A. Sloane, Jan 26 2001
EXTENSIONS
More terms from James A. Sellers, Jan 26 2001
Gary Detlefs comment changed to a formula by Robert Israel, Jun 28 2015
STATUS
approved