OFFSET
0,2
COMMENTS
Fifth column of triangle A080928.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (10,-40,80,-80,32).
FORMULA
G.f.: (1-x)*(1 - 4*x + 16*x^2 - 24*x^3 + 16*x^4)/(1-2*x)^5.
a(n) = ceiling(binomial(n+4,4)*2^(n-1)). - Zerinvary Lajos, Nov 01 2006
From Amiram Eldar, Jan 07 2022: (Start)
Sum_{n>=0} 1/a(n) = 37/3 - 16*log(2).
Sum_{n>=0} (-1)^n/a(n) = 432*log(3/2) - 523/3. (End)
MAPLE
[seq( ceil(binomial(n+4, 4)*2^(n-1)), n=0..30)]; # Zerinvary Lajos, Nov 01 2006
MATHEMATICA
Join[{1}, LinearRecurrence[{10, -40, 80, -80, 32}, {5, 30, 140, 560, 2016}, 30]] (* G. C. Greubel, Jul 23 2019 *)
PROG
(Magma) [(Ceiling(Binomial(n+4, 4)*2^(n-1))) : n in [0..30]]; // Vincenzo Librandi, Sep 22 2011
(PARI) my(x='x+O('x^30)); Vec((1-x)*(1-4*x+16*x^2-24*x^3 +16*x^4)/(1 -2*x)^5) \\ G. C. Greubel, Jul 23 2019
(Sage) ((1-x)*(1-4*x+16*x^2-24*x^3+16*x^4)/(1-2*x)^5).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jul 23 2019
(GAP) a:=[5, 30, 140, 560, 2016];; for n in [6..30] do a[n]:=10*a[n-1] -40*a[n-2]+80*a[n-3]-80*a[n-4]+32*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, Jul 23 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Feb 26 2003
STATUS
approved