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 A000746 Boustrophedon transform of triangular numbers. 3

%I

%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 on transform, J. Combin. Theory, 17A 44-54 1996 (<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="http://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(A109449(n,k)*(k+1)*(k+2)/2: k=0..n). - _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 a000746 n = sum \$ zipWith (*) (a109449_row n) \$ tail a000217_list

%o -- _Reinhard Zumkeller_, Nov 03 2013

%Y Cf. A000217, A000718.

%K nonn

%O 0,2

%A _N. J. A. Sloane_.

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Last modified January 23 09:29 EST 2019. Contains 319386 sequences. (Running on oeis4.)