A130560 Numerators of Sheffer a-sequence for Jabotinsky type triangle S2(3):=A035342.

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

Author

Wolfdieter Lang, Jul 13 2007

Keywords

• sign
• easy

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.

Examples

			Rationals: [1, 3/2, 1/2, -3/4, 3/2, -15/4, 45/4, -315/8, 315/2, -2835/4,...].
		

Links

• Wolfdieter Lang, Rationals.

Crossrefs

Cf. A006232/A006233 (a-sequence for S2(1):= Stirling2 = A048993 triangle).

a-sequence for S2(2):=A105278 is [1, 1, 0, 0, 0, ...].

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.