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Search: id:A062194
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| A062194 |
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Fifth column sequence of triangle A062139 (generalized a=2 Laguerre). |
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+0
1
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| 1, 35, 840, 17640, 352800, 6985440, 139708800, 2854051200, 59935075200, 1298593296000, 29088489830400, 674324082432000, 16183777978368000, 402104637462528000, 10339833534750720000, 275039572024369152000
(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+24*x+90*x^2+80*x^3+15*x^4)/(1-x)^11.
a(n)=A062139(n+4, 4) = (n+4)!*binomial(n+6, 6)/4!.
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-4)=(-1)^n*f(n,4,-7), (n>=4). [From Milan R. Janjic (agnus(AT)blic.net), Mar 01 2009]
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PROGRAM
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(Other) sage: [binomial(n, 6)*factorial (n-2)/factorial (4) for n in xrange(6, 22)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 07 2009]
(PARI) { f=6; for (n=0, 100, f*=n + 4; write("b062194.txt", n, " ", f*binomial(n + 6, 6)/24) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 02 2009]
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CROSSREFS
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A001710, A005990, A005461, A062193.
Sequence in context: A028024 A109508 A001724 this_sequence A004372 A080250 A014934
Adjacent sequences: A062191 A062192 A062193 this_sequence A062195 A062196 A062197
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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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