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 A231894 Boustrophedon transform of the Catalan numbers A000108. 1
 1, 3, 10, 37, 149, 648, 3039, 15401, 84619, 505500, 3287256, 23250514, 178382427, 1478782490, 13187788246, 125958159631, 1283067859947, 13886218459612, 159124624924418, 1924735353849082, 24506483918914367, 327627501208785322 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..21. D. Berry, J. Broom, D. Dixon, A. Flaherty, Umbral Calculus and the Boustrophedon Transform, 2013 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)*A000108(k+1). - Philippe Deléham, Nov 20 2013 E.g.f.: exp(2*x)*I_1(2*x)*(sec(x)+tan(x))/x, where I_1(2*x) is the modified Bessel function of the first kind. - Sergei N. Gladkovskii, Nov 19 2014 a(n) ~ n! * exp(Pi) * BesselI(1, Pi) * 2^(n+3) / Pi^(n+2). - Vaclav Kotesovec, Jun 12 2015 EXAMPLE G.f. = 1 + 3*x + 10*x^2 +37*x^3 + 149*x^4 + 648*x^5 + 3039*x^6 + 15401*x^7 + ... MAPLE A000111 := proc(n) option remember; sec(x)+tan(x) ; coeftayl(%, x=0, n)*n! ; end proc: A109449 := proc(n, k) binomial(n, k)*A000111(n-k) ; end proc: A231894 := proc(n) add( A109449(n, k)*A000108(k+1), k=0..n) ; end proc: seq(A231894(n), n=0..30) ; # R. J. Mathar, Oct 04 2014 PROG (Python) from itertools import accumulate, count, islice def A231894_gen(): # generator of terms blist, c = tuple(), 1 for i in count(1): yield (blist := tuple(accumulate(reversed(blist), initial=c)))[-1] c = c*(4*i+2)//(i+2) A231894_list = list(islice(A231894_gen(), 40)) # Chai Wah Wu, Jun 12 2022 CROSSREFS Cf. A000108, A000736, A000753, A109449. Sequence in context: A151058 A044048 A192240 * A086444 A064613 A270789 Adjacent sequences: A231891 A231892 A231893 * A231895 A231896 A231897 KEYWORD nonn AUTHOR N. J. A. Sloane, Nov 18 2013 STATUS approved

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Last modified June 21 21:50 EDT 2024. Contains 373559 sequences. (Running on oeis4.)