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 A308681 E.g.f.: (sec(x) - tan(x)) / sqrt(1 - 2*x). 0
 1, 0, 2, 7, 60, 519, 5890, 76637, 1158808, 19770383, 377036646, 7939301349, 183033429524, 4584731740471, 123994410402122, 3601004174824573, 111771076844177328, 3692510526181175583, 129364120799128910158, 4790645026641043053269, 186981399898552187792620 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Inverse boustrophedon transform of A001147. LINKS Table of n, a(n) for n=0..20. Index entries for sequences related to boustrophedon transform FORMULA a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A001147(k) * A000111(n-k). a(n) ~ (1 - sin(1/2)) * 2^(n + 1/2) * n^n / (cos(1/2) * exp(n)). - Vaclav Kotesovec, Aug 23 2021 MATHEMATICA nmax = 20; CoefficientList[Series[(Sec[x] - Tan[x])/Sqrt[1 - 2 x], {x, 0, nmax}], x] Range[0, nmax]! t[n_, 0] := (2 n - 1)!!; t[n_, k_] := t[n, k] = t[n, k - 1] - t[n - 1, n - k]; a[n_] := t[n, n]; Table[a[n], {n, 0, 20}] PROG (Python) from itertools import count, islice, accumulate from operator import sub def A308681_gen(): # generator of terms blist, m = tuple(), 1 for i in count(1): yield (blist := tuple(accumulate(reversed(blist), func=sub, initial=m)))[-1] m *= (2*i-1) A308681_list = list(islice(A308681_gen(), 30)) # Chai Wah Wu, Jun 11 2022 CROSSREFS Cf. A000111, A001147, A296792, A337445. Sequence in context: A215209 A274600 A352625 * A366328 A091687 A000892 Adjacent sequences: A308678 A308679 A308680 * A308682 A308683 A308684 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Aug 15 2021 STATUS approved

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Last modified May 27 02:41 EDT 2024. Contains 372847 sequences. (Running on oeis4.)