A231179 Boustrophedon transform of nonnegative integers, cf. A001477.

0, 1, 4, 12, 36, 120, 462, 2058, 10472, 59976, 381770, 2673374, 20422908, 169020852, 1506427678, 14385323610, 146527700944, 1585801332848, 18171944693586, 219803766565366, 2798628476670180, 37414906698747564, 524019526485293894, 7672827408344428242

Offset: 0

Author

Reinhard Zumkeller, Nov 05 2013

Keywords

• nonn

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).
• Wikipedia, Boustrophedon transform
• Index entries for sequences related to boustrophedon transform

Crossrefs

Cf. A000111, A000737, A000660, A109449, A231200.

Programs

Haskell

a231179 n = sum $ zipWith (*) (a109449_row n) [0..]

Mathematica

a[n_] := n! SeriesCoefficient[x Exp[x] (1+Sin[x]) / Cos[x], {x, 0, n}];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Jul 30 2018, after Peter Luschny *)

Python

from itertools import count, islice, accumulate
def A231179_gen(): # generator of terms
    blist = tuple()
    for i in count(0):
        yield (blist := tuple(accumulate(reversed(blist),initial=i)))[-1]
A231179_list = list(islice(A231179_gen(),30)) # Chai Wah Wu, Jun 11 2022

Formula

a(n) = A231200(n)/2.

a(n) = Sum_{k=1..n} k * A109449(n,k).

E.g.f.: x*exp(x)*(sec(x)+tan(x)). (After Sergei N. Gladkovskii in A000660.) - Peter Luschny, Oct 28 2014

a(n) = A000660(n) - A000111(n). - Sergei N. Gladkovskii, Oct 28 2014

a(n) ~ n! * exp(Pi/2) * 2^(n+1) / Pi^n. - Vaclav Kotesovec, Jun 12 2015