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Search: id:A001874
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| A001874 |
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Convolved Fibonacci numbers.
(Formerly M4174 N1738)
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+0
1
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| 1, 6, 27, 98, 315, 924, 2534, 6588, 16407, 39430, 91959, 209034, 464723, 1013292, 2171850, 4584620, 9546570, 19635840, 39940460, 80421600, 160437690, 317354740, 622844730, 1213580820, 2348773525
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)=(((-I)^n)/5!)*diff(S(n+5,x),x$5)|_{x=I}. Fifth derivative of Chebyshev S(n+5,x) polynomials evaluated at x=I (imaginary unit) multiplied by ((-I)^n)/5!. See A049310 for the S-polynomials. W. Lang, Apr 04 2007
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REFERENCES
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J. Riordan, Combinatorial Identities, Wiley, 1968, p. 101.
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LINKS
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P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
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FORMULA
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G.f.: ( 1 - x - x^2 )^-6.
a(n)=F'''''(n+5, 1)/5!, i.e. 1/5! times the 5th derivative of the (n+5)th Fibonacci polynomial evaluated at 1. - T. D. Noe (noe(AT)sspectra.com), Jan 18 2006
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MAPLE
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a := n-> (Matrix(12, (i, j)-> if (i=j-1) then 1 elif j=1 then [6, -9, -10, 30, 6, -41, -6, 30, 10, -9, -6, -1][i] else 0 fi)^n)[1, 1]; seq (a(n), n=0..24); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 15 2008]
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CROSSREFS
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Adjacent sequences: A001871 A001872 A001873 this_sequence A001875 A001876 A001877
Sequence in context: A121591 A071734 A023005 this_sequence A009061 A012320 A097553
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KEYWORD
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nonn
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AUTHOR
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njas, Simon Plouffe (simon.plouffe(AT)gmail.com)
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