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.: (sec(x) + tan(x))*(exp(x)*(x + 1/2*x^2) + 1). - Sergei N. Gladkovskii, Oct 30 2014
a(n) ~ n! * (8 + exp(Pi/2)*Pi*(4+Pi)) * 2^(n-1) / Pi^(n+1). - Vaclav Kotesovec, Jun 12 2015
MATHEMATICA
t[n_, 0] := If[n == 0, 1, n*(n+1)/2]; 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
(Haskell)
a000718 n = sum $ zipWith (*) (a109449_row n) (1 : tail a000217_list)
-- Reinhard Zumkeller, Nov 04 2013
(Python)
from itertools import accumulate, count, islice
def A000718_gen(): # generator of terms
yield 1
blist, c = (1, ), 1
for i in count(2):
yield (blist := tuple(accumulate(reversed(blist), initial=c)))[-1]
c += i
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved