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A000747

Boustrophedon transform of primes.

2, 5, 13, 35, 103, 345, 1325, 5911, 30067, 172237, 1096319, 7677155, 58648421, 485377457, 4326008691, 41310343279, 420783672791, 4553946567241, 52184383350787, 631210595896453, 8036822912123765, 107444407853010597, 1504827158220643895, 22034062627659931905

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

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 Ser. A, 76(1) (1996), 44-54 (Abstract, pdf, ps).

J. Millar, N. J. A. Sloane, and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory Ser. A, 76(1) (1996), 44-54.

Ludwig Seidel, Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [USA access only through the HATHI TRUST Digital Library]

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)*A000040(k+1). - Reinhard Zumkeller, Nov 03 2013

E.g.f.: (sec(x) + tan(x)) * Sum_{k>=0} prime(k+1)*x^k/k!. - Ilya Gutkovskiy, Jun 26 2018

MATHEMATICA

t[n_, 0] := Prime[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)

a000747 n = sum $ zipWith (*) (a109449_row n) a000040_list

-- Reinhard Zumkeller, Nov 03 2013