OFFSET
1,2
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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 (corrected by Sean A. Irvine, April 17, 2019)
R. P. Loh, A. G. Shannon, A. F. Horadam, Divisibility Criteria and Sequence Generators Associated with Fermat Coefficients, Preprint, 1980.
P. A. Piza, Fermat coefficients, Math. Mag., 27 (1954), 141-146.
FORMULA
Following Piza's definition for the Fermat coefficients: (n:c)=binomial(2n-c, c-1)/c, a(n)= Round( sum_ {c=1..n} (n:c) ). - Pab Ter (pabrlos2(AT)yahoo.com), Oct 13 2005
a(n) = rounded(sum(A258993(n,k)/(2*k+1)): k = 0..n-1). - Reinhard Zumkeller, Jun 22 2015
EXAMPLE
n...Sum_{c=1..n} (n:c).....a(n)
--------------------------------
.1........1.................1
.2........2.................2
.3........4.................4
.4........8+1/3.............8
MAPLE
FermatCoeff:=(n, c)->binomial(2*n-c, c-1)/c:seq(round(add(FermatCoeff(n, c), c=1..n)), n=1..40); # Pab Ter, Oct 13 2005
MATHEMATICA
Table[Round[Sum[Binomial[n+k, n-k]/(2*k+1), {k, 0, n-1}]], {n, 1, 35}] (* G. C. Greubel, Apr 16 2019 *)
PROG
(Haskell)
import Data.Function (on)
a000967 n = round $ sum $
zipWith ((/) `on` fromIntegral) (a258993_row n) [1, 3 ..]
-- Reinhard Zumkeller, Jun 22 2015
(PARI) {a(n) = round(sum(k=0, n-1, binomial(n+k, n-k)/(2*k+1)))}; \\ G. C. Greubel, Apr 16 2019
(Magma) [Round((&+[Binomial(n+k, n-k)/(2*k+1): k in [0..n-1]])): n in [1..35]]; // G. C. Greubel, Apr 16 2019
(Sage) [round(sum(binomial(n+k, n-k)/(2*k+1) for k in (0..n-1))) for n in (1..35)] # G. C. Greubel, Apr 16 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Pab Ter (pabrlos2(AT)yahoo.com), Oct 13 2005
STATUS
approved