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A231200
Boustrophedon transform of even numbers.
4
0, 2, 8, 24, 72, 240, 924, 4116, 20944, 119952, 763540, 5346748, 40845816, 338041704, 3012855356, 28770647220, 293055401888, 3171602665696, 36343889387172, 439607533130732, 5597256953340360, 74829813397495128, 1048039052970587788, 15345654816688856484
OFFSET
0,2
LINKS
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).
FORMULA
a(n) = Sum_{k=0..n} A109449(n,k)*k*2.
a(n) = 2*A231179(n).
E.g.f.: 2*x*exp(x)*(sec(x) + tan(x)). - Ilya Gutkovskiy, Sep 27 2017
MATHEMATICA
T[n_, k_] := SeriesCoefficient[(1+Sin[x])/Cos[x], {x, 0, n-k}] n!/k!;
a[n_] := 2 Sum[k T[n, k], {k, 0, n}];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Jun 28 2019 *)
PROG
(Haskell)
a231200 n = sum $ zipWith (*) (a109449_row n) $ [0, 2 ..]
(Python)
from itertools import accumulate, count, islice
def A231200_gen(): # generator of terms
blist = tuple()
for i in count(0, 2):
yield (blist := tuple(accumulate(reversed(blist), initial=i)))[-1]
A231200_list = list(islice(A231200_gen(), 40)) # Chai Wah Wu, Jun 12 2022
CROSSREFS
Sequence in context: A131569 A363602 A290904 * A066973 A130495 A026070
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Nov 05 2013
STATUS
approved