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A130560
Numerators of Sheffer a-sequence for Jabotinsky type triangle S2(3):=A035342.
1
1, 3, 1, -3, 3, -15, 45, -315, 315, -2835, 14175, -155925, 467775, -6081075, 42567525, -638512875, 638512875, -10854718875, 97692469875, -1856156927625, 9280784638125, -194896477400625, 2143861251406875, -49308808782358125, 147926426347074375, -3698160658676859375
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.
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
Cf. A006232/A006233 (a-sequence for S2(1):= Stirling2 = A048993 triangle).
a-sequence for S2(2):=A105278 is [1, 1, 0, 0, 0, ...].
Sequence in context: A098743 A283484 A355567 * A088105 A030708 A095709
KEYWORD
sign,easy
AUTHOR
Wolfdieter Lang, Jul 13 2007
STATUS
approved