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Search: id:A130408
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| A130408 |
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Numerators of a-sequence for Sheffer matrix A130191 (Stirling2 squared). |
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2
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| 1, 1, -1, 3, -44, 49, -9895, 3124, -54429, 2624879, -59124785, 163841201, -2508904105349, 1776678914237, -2029995134495, 175211074573961, -21557683580436716, 94127808754677868, -87882971047931164843, 161354083950193175137, -104683178840085862057001
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OFFSET
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0,4
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COMMENT
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The denomintors are found in A130409.
From the definition of the a-sequence {r(n)} one has the recurrence for (Stirling)^2= S2sq: S2sq(n,m) =(n/m)*sum(binomial(m-1+j,j)*r(j)*S2sq(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.
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LINKS
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W. Lang, Rationals and more.
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FORMULA
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a(n)=numerator(r(n)),n>=0, with the rational r(n) sequence with e.g.f. x/ln(1+ln(1+x)). {r(n)} is the a-sequence for the Sheffer matrix (Stirling2)^2 ( A130191).
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EXAMPLE
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Rationals r(n): [1,1,-1/3, 3/4,-44/15,49/3,-9895/84,3124/3,-54429/5,...].
Recurrence for (Stirling2)^2: 32=S2sq(4,2)= (4/2)*(1*1*5 + 2*1*6 +3*(-1/3)*1).
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CROSSREFS
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Cf. A006232(n)/A006233(n) (a-sequence for Stirling2 A048993).
Adjacent sequences: A130405 A130406 A130407 this_sequence A130409 A130410 A130411
Sequence in context: A114337 A009720 A076361 this_sequence A133073 A055539 A046946
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KEYWORD
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sign,frac,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jun 01 2007
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