%I #45 Jun 12 2022 12:02:51
%S 1,4,13,39,120,407,1578,7042,35840,205253,1306454,9148392,69887664,
%T 578392583,5155022894,49226836114,501420422112,5426640606697,
%U 62184720675718,752172431553308,9576956842743904,128034481788227195
%N Boustrophedon transform of triangular numbers.
%H Reinhard Zumkeller, <a href="/A000746/b000746.txt">Table of n, a(n) for n = 0..400</a>
%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>.
%H 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 (<a href="http://neilsloane.com/doc/bous.txt">Abstract</a>, <a href="http://neilsloane.com/doc/bous.pdf">pdf</a>, <a href="http://neilsloane.com/doc/bous.ps">ps</a>).
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon transform</a>.
%H <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F a(n) = Sum_{k=0..n} A109449(n,k)*(k + 1)*(k + 2)/2. - _Reinhard Zumkeller_, Nov 03 2013
%F E.g.f.: (sec(x) + tan(x))*exp(x)*(x^2 + 4*x + 2)/2. - _Sergei N. Gladkovskii_, Oct 30 2014
%F a(n) ~ n! * (Pi^2 + 8*Pi + 8) * exp(Pi/2) * 2^(n-1) / Pi^(n+1). - _Vaclav Kotesovec_, Jun 12 2015
%t 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 *)
%o (Haskell)
%o a000746 n = sum $ zipWith (*) (a109449_row n) $ tail a000217_list
%o -- _Reinhard Zumkeller_, Nov 03 2013
%o (Python)
%o from itertools import accumulate, count, islice
%o def A000746_gen(): # generator of terms
%o blist, c = tuple(), 1
%o for i in count(2):
%o yield (blist := tuple(accumulate(reversed(blist),initial=c)))[-1]
%o c += i
%o A000746_list = list(islice(A000746_gen(),40)) # _Chai Wah Wu_, Jun 12 2022
%Y Cf. A000217, A000718, A109449.
%K nonn
%O 0,2
%A _N. J. A. Sloane_