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A006504
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Coefficient of x^4 in (1-x-x^2 )^-n.
(Formerly M3895)
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5
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5, 20, 51, 105, 190, 315, 490, 726, 1035, 1430, 1925, 2535, 3276, 4165, 5220, 6460, 7905, 9576, 11495, 13685, 16170, 18975, 22126, 25650, 29575, 33930, 38745, 44051, 49880, 56265, 63240, 70840, 79101, 88060, 97755, 108225, 119510, 131651, 144690, 158670
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| G. E. Bergum and V. E. Hoggatt, Jr., Numerator polynomial coefficient array for the convolved Fibonacci sequence, Fib. Quart., 14 (1976), 43-48.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
P. Moree, Convoluted convolved Fibonacci numbers
Pieter Moree, Convoluted Convolved Fibonacci Numbers, Journal of Integer Sequences, Vol. 7 (2004), Article 04.2.2.
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FORMULA
| The coefficient of x^4 in (1-x-x^2)^{-n} is the coefficient of x^4 in (1+x+2x^2+3x^3+5x^4)^n. Using the multinomial theorem one then finds that a(n)=7n/4+59*n^2/24+3*n^3/4+n^4/24 - Pieter Moree (moree(AT)mpim-bonn.mpg.de), Sep 03 2003
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MAPLE
| A006504:=-(5-5*z+z**2)/(z-1)**5; [Conjectured by S. Plouffe in his 1992 dissertation.]
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PROG
| (Haskell)
a006504 n = n * (42 + n * (59 + n * (18 + n))) `div` 24
-- Reinhard Zumkeller, Oct 16 2011
(PARI) a(n)=7*n/4+59*n^2/24+3*n^3/4+n^4/24 \\ Charles R Greathouse IV, Oct 16, 2011
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CROSSREFS
| Sequence in context: A134481 A062158 A034133 * A007045 A102227 A173034
Adjacent sequences: A006501 A006502 A006503 * A006505 A006506 A006507
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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