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Search: id:A062193
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| A062193 |
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Fourth (unsigned) column sequence of triangle A062139 (generalized a=2 Laguerre). |
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+0
4
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| 1, 24, 420, 6720, 105840, 1693440, 27941760, 479001600, 8562153600, 159826867200, 3116623910400, 63465795993600, 1348648164864000, 29877743960064000, 689322235650048000, 16543733655601152000
(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.: (1+15*x+30*x^2+10*x^3)/(1-x)^9.
a(n)=A062139(n+3, 3) = (n+3)!*binomial(n+5, 5)/3!.
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-3)=(-1)^(n-1)*f(n,3,-6), (n>=3). [From Milan R. Janjic (agnus(AT)blic.net), Mar 01 2009]
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PROGRAM
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(Other) sage: [binomial(n, 5)*factorial (n-2)/6 for n in xrange(5, 21)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 07 2009]
(PARI) { f=2; for (n=0, 100, f*=n + 3; write("b062193.txt", n, " ", f*binomial(n + 5, 5)/6) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 02 2009]
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CROSSREFS
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A001710, A005990, A005461.
Sequence in context: A018092 A016326 A072975 this_sequence A016268 A051546 A081128
Adjacent sequences: A062190 A062191 A062192 this_sequence A062194 A062195 A062196
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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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