A230953 - OEIS

%I #21 Jun 12 2022 12:23:32

%S 3,8,20,53,154,505,1944,8651,44046,252271,1605874,11245261,85907084,

%T 710970323,6336648426,60510526207,616355168958,6670526004559,

%U 76438597647616,924584128977111,11772170758462928,157382330019694067,2204239468545788024,32275035859881159165

%N Boustrophedon transform of odd primes, cf. A065091.

%H Reinhard Zumkeller, <a href="/A230953/b230953.txt">Table of n, a(n) for n = 0..400</a>

%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>

%H 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 (<a href="http://neilsloane.com/doc/bous.txt">Abstract</a>, <a href="http://neilsloane.com/doc/bous.pdf">pdf</a>, <a href="http://neilsloane.com/doc/bous.ps">ps</a>).

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon transform</a>

%H <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>

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

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

%t 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 *)

%o (Haskell)

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

%o (Python)

%o from itertools import accumulate, count, islice

%o from sympy import prime

%o def A230953_gen(): # generator of terms

%o     blist = tuple()

%o     for i in count(2):

%o         yield (blist := tuple(accumulate(reversed(blist),initial=prime(i))))[-1]

%o A230953_list = list(islice(A230953_gen(),40)) # _Chai Wah Wu_, Jun 12 2022

%Y Cf. A000747, A230956, A230954, A230955.

%K nonn

%O 0,1

%A _Reinhard Zumkeller_, Nov 03 2013