The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A000736 Boustrophedon transform of Catalan numbers 1, 1, 1, 2, 5, 14, ... 4
 1, 2, 4, 10, 32, 120, 513, 2455, 13040, 76440, 492231, 3465163, 26530503, 219754535, 1959181266, 18710532565, 190588702776, 2062664376064, 23636408157551, 285900639990875, 3640199365715769, 48665876423760247 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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). N. J. A. Sloane, Transforms Wikipedia, Boustrophedon transform FORMULA E.g.f.: (sec(x) + tan(x))*(integral(exp(2*x)*(BesselI(0,2*x)-BesselI(1,2*x)),x)+1). - Sergei N. Gladkovskii, Oct 30 2014 a(n) ~ n! * (6/Pi+2*exp(Pi)*((2-1/Pi)*BesselI(0,Pi)-2*BesselI(1,Pi))) * 2^n / Pi^n. - Vaclav Kotesovec, Oct 30 2014 MAPLE egf := (sec(x/2)+tan(x/2))*(exp(x)*((x-1/2)*BesselI(0, x)-x*BesselI(1, x))+3/2); s := n -> 2^n*n!*coeff(series(egf, x, n+2), x, n); seq(s(n), n=0..22); # Peter Luschny, Oct 30 2014, after Sergei N. Gladkovskii MATHEMATICA CoefficientList[Series[1/2*(3 + E^(2*x)*((4*x-1)*BesselI[0, 2*x] - 4*x*BesselI[1, 2*x]))*(Sec[x] + Tan[x]), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Oct 30 2014, after Peter Luschny *) t[n_, 0] := If[n == 0, 1, CatalanNumber[n - 1]]; 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) a000736 n = sum \$ zipWith (*) (a109449_row n) (1 : a000108_list) -- Reinhard Zumkeller, Nov 05 2013 (Python) from itertools import accumulate, count, islice def A000736_gen(): # generator of terms     yield 1     blist, c = (1, ), 1     for i in count(0):         yield (blist := tuple(accumulate(reversed(blist), initial=c)))[-1]         c = c*(4*i+2)//(i+2) A000736_list = list(islice(A000736_gen(), 40)) # Chai Wah Wu, Jun 12 2022 CROSSREFS Cf. A000108, A000753, A109449. Sequence in context: A071954 A352279 A120017 * A263663 A176006 A263664 Adjacent sequences:  A000733 A000734 A000735 * A000737 A000738 A000739 KEYWORD nonn AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 3 18:04 EDT 2022. Contains 355055 sequences. (Running on oeis4.)