A230953 Boustrophedon transform of odd primes, cf. A065091.

3, 8, 20, 53, 154, 505, 1944, 8651, 44046, 252271, 1605874, 11245261, 85907084, 710970323, 6336648426, 60510526207, 616355168958, 6670526004559, 76438597647616, 924584128977111, 11772170758462928, 157382330019694067, 2204239468545788024, 32275035859881159165

Offset: 0

Author

Reinhard Zumkeller, Nov 03 2013

Keywords

• nonn

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).
• Wikipedia, Boustrophedon transform
• Index entries for sequences related to boustrophedon transform

Crossrefs

Cf. A000747, A230956, A230954, A230955.

Programs

Haskell

a230953 n = sum $ zipWith (*) (a109449_row n) $ tail a000040_list

Mathematica

t[n_, 0] := Prime[n+2]; 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 *)

Python

from itertools import accumulate, count, islice
from sympy import prime
def A230953_gen(): # generator of terms
    blist = tuple()
    for i in count(2):
        yield (blist := tuple(accumulate(reversed(blist),initial=prime(i))))[-1]
A230953_list = list(islice(A230953_gen(),40)) # Chai Wah Wu, Jun 12 2022

Formula

a(n) = Sum_{k=0..n} A109449(n,k)*A000040(k+2).

E.g.f.: (sec(x) + tan(x)) * Sum_{k>=0} prime(k+2)*x^k/k!. - Ilya Gutkovskiy, Jun 26 2018