OFFSET
1,1
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
G. E. Bergum and V. E. Hoggatt, Jr., Numerator polynomial coefficient array for the convolved Fibonacci sequence, Fib. Quart., 14 (1976), 43-44. (Annotated scanned copy)
G. E. Bergum and V. E. Hoggatt, Jr., Numerator polynomial coefficient array for the convolved Fibonacci sequence, Fib. Quart., 14 (1976), 43-48.
M. Janjic, Hessenberg Matrices and Integer Sequences , J. Int. Seq. 13 (2010) # 10.7.8, section 3.
P. Moree, Convoluted convolved Fibonacci numbers, arXiv:math/0311205 [math.CO], 2003.
Pieter Moree, Convoluted Convolved Fibonacci Numbers, Journal of Integer Sequences, Vol. 7 (2004), Article 04.2.2.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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
a(n) = n*(n+1)*(n+3)*(n+14)/4!. - Alois P. Heinz, Jan 21 2017
MAPLE
A006504:=-(5-5*z+z**2)/(z-1)**5; # conjectured by Simon Plouffe in his 1992 dissertation
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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved