OFFSET
1,1
COMMENTS
The p-th differences of a sequence a(n) are Delta^p(n) = sum_{l=0}^p (-1)^(l+p)*binomial(p,l)*a(n+l).
Setting this equal to 2*a(n) as demanded gives a recurrence with coefficients tabulated here,
a(n+p) = sum_{s=1..p} T(p,s)*a(n+p-s).
FORMULA
EXAMPLE
The triangle starts in row p=0 as:
.3; (p=1, example A000244, a(n+1)=3*a(n)
.4,.-6,..4,...1;
.5,-10,.10,..-5,..3;
.6,-15,.20,.-15,..6,...1;
.7,-21,.35,.-35,.21,..-7,..3;
.8,-28,.56,.-70,.56,.-28,..8,..1;
.9,-36,.84,-126,126,.-84,.36,.-9,.3;
10,-45,120,-210,252,-210,120,-45,10,1;
CROSSREFS
KEYWORD
AUTHOR
Paul Curtz, Jun 25 2008
EXTENSIONS
Edited by R. J. Mathar, Mar 02 2010
STATUS
approved