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 A118928 a(n) = Sum_{k=0..floor(n/2)} C(n-k,k)*C(n-k,k+1)/(n-k) * a(k), with a(0)=1. 1
 1, 1, 1, 2, 4, 8, 17, 38, 92, 238, 643, 1790, 5076, 14573, 42241, 123484, 364052, 1082602, 3247759, 9829820, 30019326, 92517644, 287805801, 903822922, 2865339252, 9168572009, 29601077285, 96377791839, 316264456921 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Invariant column vector V under matrix product A089732 *V = V: a(n) = Sum_{k=0,[n/2]} A089732 (n,k)*a(k), where A089732(n,k) = number of peakless Motzkin paths of length n having k (1,1) steps. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 FORMULA a(n) = Sum_{k=0..floor(n/2)} C(n-k,k)*C(n-k,k+1)/(n-k) * a(k), with a(0)=1. MATHEMATICA a[n_]:= a[n]= If[n==0, 1, Sum[Binomial[n-k, k]*Binomial[n-k, k+1]*a[k]/(n-k), {k, 0, Floor[n/2]}]]; Table[a[n], {n, 0, 30}] (* G. C. Greubel, Nov 24 2021 *) PROG (PARI) {a(n)=if(n==0, 1, sum(k=0, n\2, binomial(n-k, k)*binomial(n-k, k+1)/(n-k)*a(k)))} (Sage) @CachedFunction def A118928(n): if (n==0): return 1 else: return sum( binomial(n-k, k)*binomial(n-k, k+1)*A118928(k)/(n-k) for k in (0..n//2) ) [A118928(n) for n in (0..30)] # G. C. Greubel, Nov 24 2021 CROSSREFS Cf. A089732. Sequence in context: A340776 A090901 A101516 * A325921 A049312 A132043 Adjacent sequences: A118925 A118926 A118927 * A118929 A118930 A118931 KEYWORD nonn AUTHOR Paul D. Hanna, May 06 2006 STATUS approved

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Last modified December 10 09:19 EST 2023. Contains 367704 sequences. (Running on oeis4.)