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 (1996), 44-54 (Abstract, pdf, ps).
N. J. A. Sloane, Transforms.
Wikipedia, Boustrophedon transform.
FORMULA
From Reinhard Zumkeller, Nov 02 2013: (Start)
a(n) = Sum_{k=0..n} A109449(n,k)*(2*k + 1). (End)
E.g.f.: (sec(x) + tan(x))*exp(x)*(2*x + 1). - Sergei N. Gladkovskii, Oct 30 2014
a(n) ~ n! * (Pi+1) * exp(Pi/2) * 2^(n+2) / Pi^(n+1). - Vaclav Kotesovec, Oct 30 2014
MATHEMATICA
CoefficientList[Series[(Sec[x]+Tan[x])*E^x*(2*x+1), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Oct 30 2014 after Sergei N. Gladkovskii *)
t[n_, 0] := 2n + 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
(Haskell)
a000754 n = sum $ zipWith (*) (a109449_row n) [1, 3 ..]
-- Reinhard Zumkeller, Nov 02 2013
(Python)
from itertools import accumulate, count, islice
def A000754_gen(): # generator of terms
blist = tuple()
for i in count(1, 2):
yield (blist := tuple(accumulate(reversed(blist), initial=i)))[-1]
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
STATUS
approved