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 A110489 Row sums of a triangle based on the Catalan numbers. 2
 1, 2, 5, 14, 43, 142, 497, 1828, 7037, 28326, 119361, 527748, 2454929, 12041410, 62354641, 340840118, 1963757863, 11896370734, 75549183725, 501393978466, 3467199478543, 24916100775758, 185646100106929, 1431332539961350 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums of A110488. LINKS G. C. Greubel, Table of n, a(n) for n = 0..595 FORMULA a(n) = Sum_{k=0..n} Sum_{j=0..(n-k)} 2*(j+1)*(k-1)^j*C(2*(n-k)+1, n-k-j)/ (n-k+j+2). MATHEMATICA T[n_, 0] := CatalanNumber[n]; T[n_, 1] := CatalanNumber[n]; T[n_, n_] := 1; T[n_, k_] := Sum[2*(j + 1)*(k - 1)^j*Binomial[2 (n - k) + 1, n - k - j]/(n - k + j + 2), {j, 0, n - k}]; Table[Sum[T[n, k], {k, 0, n}], {n, 0, 50}] (* G. C. Greubel, Aug 29 2017 *) PROG (PARI) a(n) = sum(k=0, n, sum(j=0, (n-k), 2*(j+1)*(k-1)^j*binomial(2*(n-k)+1, n-k-j)/ (n-k+j+2))); \\ Michel Marcus, Aug 29 2017 CROSSREFS Cf. A110488. Sequence in context: A126566 A112808 A088927 * A005425 A035349 A155888 Adjacent sequences:  A110486 A110487 A110488 * A110490 A110491 A110492 KEYWORD easy,nonn AUTHOR Paul Barry, Jul 22 2005 STATUS approved

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Last modified April 16 04:49 EDT 2021. Contains 343030 sequences. (Running on oeis4.)