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A000746 Boustrophedon transform of triangular numbers. 4
1, 4, 13, 39, 120, 407, 1578, 7042, 35840, 205253, 1306454, 9148392, 69887664, 578392583, 5155022894, 49226836114, 501420422112, 5426640606697, 62184720675718, 752172431553308, 9576956842743904, 128034481788227195 (list; graph; refs; listen; history; text; internal format)
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 (1996), 44-54 (Abstract, pdf, ps).
N. J. A. Sloane, Transforms.
FORMULA
a(n) = Sum_{k=0..n} A109449(n,k)*(k + 1)*(k + 2)/2. - Reinhard Zumkeller, Nov 03 2013
E.g.f.: (sec(x) + tan(x))*exp(x)*(x^2 + 4*x + 2)/2. - Sergei N. Gladkovskii, Oct 30 2014
a(n) ~ n! * (Pi^2 + 8*Pi + 8) * exp(Pi/2) * 2^(n-1) / Pi^(n+1). - Vaclav Kotesovec, Jun 12 2015
MATHEMATICA
t[n_, 0] := (n + 1) (n + 2)/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)
a000746 n = sum $ zipWith (*) (a109449_row n) $ tail a000217_list
-- Reinhard Zumkeller, Nov 03 2013
(Python)
from itertools import accumulate, count, islice
def A000746_gen(): # generator of terms
blist, c = tuple(), 1
for i in count(2):
yield (blist := tuple(accumulate(reversed(blist), initial=c)))[-1]
c += i
A000746_list = list(islice(A000746_gen(), 40)) # Chai Wah Wu, Jun 12 2022
CROSSREFS
Sequence in context: A290929 A121192 A133409 * A271012 A272581 A342159
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)