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 A192653 Binomial convolution of the Floor-Sqrt transform of Catalan numbers. 0
 1, 2, 4, 10, 28, 82, 264, 866, 2984, 10476, 37500, 135916, 496242, 1821384, 6712394, 24818020, 92016874, 342043052, 1274461144, 4759439600, 17812520318, 66803249358, 251038475982, 945202437760, 3565529448118, 13474452634994, 51010511291144, 193438196953970 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..27. FORMULA a(n) = sum(binomial(n,k)*floor(sqrt(binomial(2*k,k)/(k+1)))*floor(sqrt(binomial(2*n-2*k,n-k)/(n-k+1))),k=0..n). MATHEMATICA Table[Sum[Binomial[n, k]Floor[Sqrt[Binomial[2k, k]/(k+1)]]Floor[Sqrt[Binomial[2n-2k, n-k]/(n-k+1)]], {k, 0, n}], {n, 0, 100}] PROG (Maxima) makelist(sum(binomial(n, k)*floor(sqrt(binomial(2*k, k)/(k+1)))*floor(sqrt(binomial(2*n-2*k, n-k)/(n-k+1))), k, 0, n), n, 0, 24); CROSSREFS Sequence in context: A187256 A148110 A149823 * A149824 A331938 A302146 Adjacent sequences: A192650 A192651 A192652 * A192654 A192655 A192656 KEYWORD nonn AUTHOR Emanuele Munarini, Jul 07 2011 STATUS approved

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Last modified September 9 16:11 EDT 2024. Contains 375765 sequences. (Running on oeis4.)