OFFSET
0,2
COMMENTS
This rational a-sequence leads to the following recurrence for triangle S2(3):=A035342: A035342(n,m)=(n/m)*sum(binomial(m-1+j,m-1)*a(j)*A035342(n-1,m-1+j),j=0..n-m), n>=m>=1.
For the notion of the a-sequence for a Sheffer matrix see the W. Lang link under A006232. Here the a-sequence is called r(n) because it is a sequence of rationals.
Denominators are numerators of (2^n)/n!, see A001316 and the M. Bouayoun comment.
For the notion of the a-sequence for a Sheffer matrix see the W. Lang link under A006233. Here the a-sequence is called r(n) because it is a sequence of rationals.
LINKS
Wolfdieter Lang, Rationals.
FORMULA
E.g.f.: (1+x)^2/(1+x/2).
a(n) = numerator(r(n)), n>=0, with r(0)=1, r(1)=3/2, r(n)=((-1)^n)*n!/2^n, n>=2.
EXAMPLE
Rationals: [1, 3/2, 1/2, -3/4, 3/2, -15/4, 45/4, -315/8, 315/2, -2835/4,...].
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Wolfdieter Lang, Jul 13 2007
STATUS
approved