OFFSET
0,2
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..400
Peter Luschny, An old operation on sequences: the Seidel transform
J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory, 17A 44-54 1996 (Abstract, pdf, ps).
N. J. A. Sloane, Transforms
Wikipedia, Boustrophedon transform
FORMULA
E.g.f.: (1 + x)*(tan x + sec x)*exp(x).
a(n) ~ n! * (Pi + 2)*exp(Pi/2)*2^(n+1)/Pi^(n+1). - Vaclav Kotesovec, Oct 02 2013
MATHEMATICA
CoefficientList[Series[(1+x)*(Tan[x]+1/Cos[x])* E^x, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 02 2013 *)
t[n_, 0] := n + 1; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 30, 0] (* Jean-François Alcover, Feb 12 2016 *)
PROG
(Sage) # Algorithm of L. Seidel (1877)
def A000737_list(n) :
R = []; A = {-1:0, 0:0}
k = 0; e = 1
for i in range(n) :
Am = i+1
A[k + e] = 0
e = -e
for j in (0..i) :
Am += A[k]
A[k] = Am
k += e
# To trace the algorithm remove the comment sign.
# print([A[z] for z in (-i//2..i//2)])
R.append(A[e*i//2])
return R
A000737_list(10) # Peter Luschny, Jun 02 2012
(Haskell)
a000737 n = sum $ zipWith (*) (a109449_row n) [1..]
-- Reinhard Zumkeller, Nov 05 2013
(Python)
from itertools import count, accumulate, islice
def A000737_gen(): # generator of terms
blist = tuple()
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=i)))[-1]
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved