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Search: id:A062195
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| A062195 |
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Sixth (unsigned) column sequence of triangle A062139 (generalized a=2 Laguerre). |
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+0
2
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| 1, 48, 1512, 40320, 997920, 23950080, 570810240, 13699445760, 333923990400, 8310997094400, 211930425907200, 5548723878297600, 149353151057510400, 4135933413900288000, 117874102296158208000
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,100
Index entries for sequences related to Laguerre polynomials
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FORMULA
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E.g.f.: N(2;5, x)/(1-x)^13 with N(2;5, x) := sum(A062196(5, k)*x^k, k=0..5) = 1+35*x+210*x^2+350*x^3+175*x^4+21*x^5.
a(n)=A062139(n+5, 5) = (n+5)!*binomial(n+7, 7)/5!.
If we define f(n,i,x)= sum(sum(binomial(k,j)*stirling1(n,k)*stirling2(j,i)*x^(k-j),j=i..k),k=i..n) then a(n-5)=(-1)^(n-1)*f(n,5,-8), (n>=5). [From Milan R. Janjic (agnus(AT)blic.net), Mar 01 2009]
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PROGRAM
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(PARI) { f=24; for (n=0, 100, f*=n + 5; write("b062195.txt", n, " ", f*binomial(n + 7, 7)/120) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 02 2009]
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CROSSREFS
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A001710, A005990, A005461, A062193-4.
Sequence in context: A089272 A004362 A160368 this_sequence A004386 A076003 A008845
Adjacent sequences: A062192 A062193 A062194 this_sequence A062196 A062197 A062198
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jun 19 2001
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