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Search: id:A130560
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| A130560 |
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Numerators of Sheffer a-sequence for Jabotinsky type triangle S2(3):=A035342. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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.
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LINKS
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W. Lang, Rationals.
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FORMULA
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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.
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EXAMPLE
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Rationals: [1, 3/2, 1/2, -3/4, 3/2, -15/4, 45/4, -315/8, 315/2, -2835/4,...].
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CROSSREFS
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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: A038573 A133579 A098743 this_sequence A088105 A030708 A095709
Adjacent sequences: A130557 A130558 A130559 this_sequence A130561 A130562 A130563
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KEYWORD
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sign,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jul 13 2007
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