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A000754 Boustrophedon transform of odd numbers. 4
1, 4, 12, 33, 96, 317, 1218, 5425, 27608, 158129, 1006574, 7048657, 53847420, 445643681, 3971876930, 37928628529, 386337833232, 4181155148673, 47912508680086, 579538956964241, 7378919177090244, 98648882783190305 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = Sum_{k=0..n} A116666(n+1,k)*A000111(n-k). - Reinhard Zumkeller, Nov 02 2013

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

a(n) = Sum_{k=0..n} A109449(n,k)*(2*k + 1). - Reinhard Zumkeller, Nov 02 2013

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

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

MATHEMATICA

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

t[n_, 0] := 2n + 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-Fran├žois Alcover, Feb 12 2016 *)

PROG

(Haskell)

a000754 n = sum $ zipWith (*) (a109449_row n) [1, 3 ..]

-- Reinhard Zumkeller, Nov 02 2013

CROSSREFS

Cf. A005408.

Sequence in context: A293064 A219092 A135254 * A119683 A135373 A209818

Adjacent sequences:  A000751 A000752 A000753 * A000755 A000756 A000757

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 19 16:56 EST 2018. Contains 299356 sequences. (Running on oeis4.)