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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 on transform, J. Combin. Theory, 17A 44-54 1996 (Abstract, pdf, ps).

N. J. A. Sloane, Transforms

Wikipedia, Boustrophedon_transform

Index entries for sequences related to 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

CROSSREFS

Cf. A000108, A000753, A109449.

Sequence in context: A151400 A071954 A120017 * A263663 A176006 A263664

Adjacent sequences:  A000733 A000734 A000735 * A000737 A000738 A000739

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Simon Plouffe

STATUS

approved

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Last modified August 18 14:30 EDT 2018. Contains 313832 sequences. (Running on oeis4.)