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 A186334 A transform of the Catalan numbers. 0
 1, 1, 3, 5, 12, 24, 56, 123, 291, 677, 1637, 3954, 9757, 24171, 60648, 152929, 388822, 993216, 2551808, 6582899, 17055507, 44341141, 115671498, 302627130, 793951897, 2088103609, 5504504961, 14541271283, 38489869502, 102066761622, 271122837895 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Hankel transform is A094967(n+1) (F(2n+1) repeated). LINKS Table of n, a(n) for n=0..30. FORMULA a(n)=sum{k=0..n, sum{j=0..n, binomial(k-j,n-k-j)*binomial(k,j)*if(n-k-j>=0, A000108(n-k-j),0)}} Conjecture: (n+2)*a(n) +2*(-n-1)*a(n-1) +(-5*n+4)*a(n-2) +2*(3*n-4)*a(n-3) +5*(n-2)*a(n-4)=0. - R. J. Mathar, Nov 07 2014 a(n) ~ 21^(1/4) * ((1+sqrt(21))/2)^(n + 5/2) / (8 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Oct 30 2017 MATHEMATICA Table[Sum[Sum[Binomial[k-j, n-k-j] * Binomial[k, j] * If[n-k-j>=0, CatalanNumber[n-k-j], 0], {j, 0, n}], {k, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, Oct 30 2017 *) CROSSREFS Cf. A186335. Sequence in context: A027246 A185087 A090345 * A303587 A151524 A030270 Adjacent sequences: A186331 A186332 A186333 * A186335 A186336 A186337 KEYWORD nonn,easy AUTHOR Paul Barry, Feb 18 2011 STATUS approved

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Last modified August 7 03:39 EDT 2024. Contains 375008 sequences. (Running on oeis4.)