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A141417
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(-1)^(n+1)*A091137(n)*a(0,n), where a(i,j) = int_{x=i..i+1} x*(x-1)*(x-2)*..*(x-j+1)/j! dx.
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9
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-1, 1, 1, 1, 19, 27, 863, 1375, 33953, 57281, 3250433, 5675265, 13695779093, 24466579093, 132282840127, 240208245823, 111956703448001, 205804074290625, 151711881512390095, 281550972898020815, 86560056264289860203, 161867055619224199787, 20953816286242674495191, 39427936010479474495191
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| This is the row i=0 of an array defined as T(i,j) = (-1)^(i+j+1)*A091137(j)*a(i,j), columns j>=0, which starts
-1, 1, 1, 1, 19, 27, 863
1, -3, 5, 1, 11, 11, 271
-1, 5, -23, 9, 19, 11, 191
1, -7, 53, -55, 251, 27, 271
-1, 9, -95, 161,-1901, 475, 863
1,-11, 149, -351, 6731,-4277,19087
The first two rows are related via T(0,j) = A027760(j)*T(0,j-1)-T(1,j).
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REFERENCES
| P. Curtz, Integration .., note 12, C.C.S.A., Arcueil, 1969.
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FORMULA
| a(i,j)=a(i-1,j)+a(i-1,j-1), see reference page 33.
(q+1-j)*sum_{j=0..q} a(i,j)*(-1)^(q-j)= binomial(i,q), see reference page 35.
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MAPLE
| A091137 := proc(n) local a, i, p ; a := 1 ; for i from 1 do p := ithprime(i) ; if p > n+1 then break; fi; a := a*p^floor(n/(p-1)) ; od: a ; end proc:
A048994 := proc(n, k) combinat[stirling1](n, k) ; end proc:
a := proc(i, j) add(A048994(j, k)*x^k, k=0..j) ; int(%, x=i..i+1) ; %/j! ; end proc:
A141417 := proc(n) (-1)^(n+1)*A091137(n)*a(0, n) ; end proc:
seq(A141417(n), n=0..40) ; # R. J. Mathar, Nov 17 2010
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CROSSREFS
| Cf. A141047, A140811, A140825.
Sequence in context: A146651 A146808 A147232 * A069529 A138335 A173639
Adjacent sequences: A141414 A141415 A141416 * A141418 A141419 A141420
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KEYWORD
| sign
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Aug 05 2008
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EXTENSIONS
| Removed erroneous formula linking A091137 and A002196; added more terms and program - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 17 2010
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