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

%I A130560 #10 Nov 09 2019 10:44:00
%S A130560 1,3,1,-3,3,-15,45,-315,315,-2835,14175,-155925,467775,-6081075,
%T A130560 42567525,-638512875,638512875,-10854718875,97692469875,
%U A130560 -1856156927625,9280784638125,-194896477400625,2143861251406875,-49308808782358125,147926426347074375,-3698160658676859375
%N A130560 Numerators of Sheffer a-sequence for Jabotinsky type triangle S2(3):=A035342.
%C A130560 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.
%C A130560 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.
%C A130560 Denominators are numerators of (2^n)/n!, see A001316 and the M. Bouayoun comment.
%C A130560 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.
%H A130560 Wolfdieter Lang, <a href="/A130560/a130560.txt">Rationals. </a>
%F A130560 E.g.f.: (1+x)^2/(1+x/2).
%F A130560 a(n) = numerator(r(n)), n>=0, with r(0)=1, r(1)=3/2, r(n)=((-1)^n)*n!/2^n, n>=2.
%e A130560 Rationals: [1, 3/2, 1/2, -3/4, 3/2, -15/4, 45/4, -315/8, 315/2, -2835/4,...].
%Y A130560 Cf. A006232/A006233 (a-sequence for S2(1):= Stirling2 = A048993 triangle).
%Y A130560 a-sequence for S2(2):=A105278 is [1, 1, 0, 0, 0, ...].
%K A130560 sign,easy
%O A130560 0,2
%A A130560 _Wolfdieter Lang_, Jul 13 2007