

A118928


a(n) = Sum_{k=0..floor(n/2)} C(nk,k)*C(nk,k+1)/(nk) * 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
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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



FORMULA

a(n) = Sum_{k=0..floor(n/2)} C(nk,k)*C(nk,k+1)/(nk) * a(k), with a(0)=1.


MATHEMATICA

a[n_]:= a[n]= If[n==0, 1, Sum[Binomial[nk, k]*Binomial[nk, k+1]*a[k]/(nk), {k, 0, Floor[n/2]}]];


PROG

(PARI) {a(n)=if(n==0, 1, sum(k=0, n\2, binomial(nk, k)*binomial(nk, k+1)/(nk)*a(k)))}
(Sage)
@CachedFunction
if (n==0): return 1
else: return sum( binomial(nk, k)*binomial(nk, k+1)*A118928(k)/(nk) for k in (0..n//2) )


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



