A110490 Diagonal sums of a triangle based on the Catalan numbers.

1, 1, 3, 7, 20, 59, 185, 600, 2003, 6833, 23727, 83606, 298313, 1076155, 3920823, 14416987, 53482012, 200151737, 755894009, 2882782933, 11115015138, 43400057683, 172016505877, 694208585423, 2863726993748, 12130698802645

Offset

0,3

Comments

Diagonal sums of A110488.

Links

G. C. Greubel, Table of n, a(n) for n = 0..675

Formula

a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..(n-2*k)} 2*(j+1)*(k-1)^j*C(2*(n-2*k)+1, n-2*k-j)/(n-2*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}]; Join[{1, 1}, Table[Sum[T[n - k, k], {k, 0, n}], {n, 2, 50}]] (* G. C. Greubel, Aug 29 2017 *)

Crossrefs

Cf. A110488.

Sequence in context: A084204 A030238 A132364 * A132868 A357792 A361625

Adjacent sequences: A110487 A110488 A110489 * A110491 A110492 A110493

Keyword

easy,nonn

Author

Paul Barry, Jul 22 2005

Status

approved