OFFSET
0,3
COMMENTS
Row sums of the absolute values of the triangle of Stirling1(n,k)*Bell(k)^2:
1;
0, 1;
0, -1, 4;
0, 2, -12, 25;
0, -6, 44, -150, 225;
0, 24, -200, 875, -2250, 2704;
0, -120, 1096, -5625, 19125, -40560, 41209;
0, 720, -7056, 40600, -165375, 473200, -865389, 769129;
... - R. J. Mathar, Jan 27 2017
FORMULA
a(n) = exp(-2)*Sum_{r,s>=0} [r*s]^n/(r!*s!), where [m]^n = m*(m+1)*...*(m+n-1) is the rising factorial.
E.g.f.: Sum_{n>=0} exp( 1/(1-x)^n - 2 ) / n!. - Paul D. Hanna, Jul 25 2018
MAPLE
with(combinat): seq(sum(abs(stirling1(n, k))*bell(k)^2, k=0..n), n=0..19); # Emeric Deutsch, Oct 08 2006
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladeta Jovovic, Sep 15 2006, Sep 19 2006
EXTENSIONS
More terms from Emeric Deutsch, Oct 08 2006
STATUS
approved