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A230953 Boustrophedon transform of odd primes, cf. A065091. 7
3, 8, 20, 53, 154, 505, 1944, 8651, 44046, 252271, 1605874, 11245261, 85907084, 710970323, 6336648426, 60510526207, 616355168958, 6670526004559, 76438597647616, 924584128977111, 11772170758462928, 157382330019694067, 2204239468545788024, 32275035859881159165 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
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).
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
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 *)
PROG
(Haskell)
a230953 n = sum $ zipWith (*) (a109449_row n) $ tail a000040_list
(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
CROSSREFS
Sequence in context: A027220 A305823 A333679 * A026995 A018035 A271843
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Nov 03 2013
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)