A110489 Row sums of a triangle based on the Catalan numbers.

1, 2, 5, 14, 43, 142, 497, 1828, 7037, 28326, 119361, 527748, 2454929, 12041410, 62354641, 340840118, 1963757863, 11896370734, 75549183725, 501393978466, 3467199478543, 24916100775758, 185646100106929, 1431332539961350

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: A112808 A369158 A088927 * A005425 A035349 A155888

Adjacent sequences: A110486 A110487 A110488 * A110490 A110491 A110492

Keyword

easy,nonn

Author

Paul Barry, Jul 22 2005

Status

approved