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 A298300 Analog of Motzkin numbers for Coxeter type D. 1
 1, 4, 11, 31, 87, 246, 699, 1996, 5723, 16468, 47533, 137567, 399073, 1160082, 3378483, 9855207, 28790403, 84218052, 246651729, 723165765, 2122391109, 6234634266, 18330019029, 53932825926, 158802303429, 467898288676, 1379485436579, 4069450219561 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 LINKS FORMULA a(n) = A002426(n-1) + A290380(n) (the latter being extended by A290380(2)=0). Conjectural algebraic equation: 3*t+2+(3*t^2+5*t-2)*f(t)+(3*t^3-t^2)*f(t)^2 = 0. From Peter Luschny, Jan 23 2018: (Start) a(n) = hypergeom([(1-n)/2,1-n/2],[1],4]+(n-2)*hypergeom([1-n/2,3/2-n/2],[2],4). a(n) = G(n-1,1-n,-1/2) + G(n-2,1-n,-1/2)*(n-2)/(n-1) where G(n,a,x) denotes the n-th Gegenbauer polynomial. (End) MATHEMATICA b[n_] := Hypergeometric2F1[(1 - n)/2, 1 - n/2, 1, 4]; c[n_] := (n-2) Hypergeometric2F1[1 - n/2, 3/2 - n/2, 2, 4]; Table[b[n] + c[n], {n, 2, 29}] (* Peter Luschny, Jan 23 2018 *) PROG (Sage) def a(n):      return (sum(ZZ(n - 2) / i * binomial(2 * i - 2, i - 1) *          binomial(n - 2, 2 * i - 2)                  for i in range(1, floor(n / 2) + 1)) +              sum(binomial(n - 1, k) * binomial(n - 1 - k, k)                  for k in range(floor((n - 1) / 2) + 1))) CROSSREFS Cf. A001006 (type A), A002426 (type B), A290380. Sequence in context: A165993 A192312 A004080 * A027115 A077995 A276293 Adjacent sequences:  A298297 A298298 A298299 * A298301 A298302 A298303 KEYWORD nonn AUTHOR F. Chapoton, Jan 16 2018 STATUS approved

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Last modified October 16 15:31 EDT 2019. Contains 328101 sequences. (Running on oeis4.)