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A000753 Boustrophedon transform of Catalan numbers. 4
1, 2, 5, 16, 59, 243, 1101, 5461, 29619, 175641, 1137741, 8031838, 61569345, 510230087, 4549650423, 43452408496, 442620720531, 4790322653809, 54893121512453, 663974736739232, 8453986695437957, 113021461431438475 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..400

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

Index entries for sequences related to boustrophedon transform

FORMULA

a(n) = Sum_{k=0..n} A109449(n,k)*A000108(k). - Reinhard Zumkeller, Nov 05 2013

E.g.f.: (sec(x) + tan(x))*exp(2*x)*(BesselI(0,2*x) - BesselI(1,2*x)). - Sergei N. Gladkovskii, Oct 30 2014

a(n) ~ n! * exp(Pi) * (BesselI(0, Pi) - BesselI(1, Pi)) * 2^(n+2) / Pi^(n+1). - Vaclav Kotesovec, Oct 30 2014

MATHEMATICA

CoefficientList[Series[E^(2*x) * (BesselI[0, 2*x] - BesselI[1, 2*x]) * (Sec[x] + Tan[x]), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Oct 30 2014 after Sergei N. Gladkovskii *)

PROG

(Haskell)

a000753 n = sum $ zipWith (*) (a109449_row n) a000108_list

-- Reinhard Zumkeller, Nov 05 2013

CROSSREFS

Cf. A000736.

Sequence in context: A243326 A185143 A280760 * A007878 A019589 A087949

Adjacent sequences:  A000750 A000751 A000752 * A000754 A000755 A000756

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 13 14:58 EST 2017. Contains 295958 sequences.