A098509 -id:A098509 - cp's OEIS frontend

A098512 Second column and subdiagonal of number triangle A098509.

1, 1, 1, 5, 7, 42, 22, 429, 715, 4862, 8398, 58786, 52003, 742900, 1337220, 646323, 17678835, 129644790, 79606450, 1767263190, 328206021, 8155422340, 45741281820, 343059613650, 107492012277, 4861946401452, 9183676536076

Offset: 0

Paul Barry, Sep 11 2004

Cf. A093526, A093527, A000108.

C := n -> binomial(2*n,n)/(n+1):
A098512 := n -> C(n)/igcd(n,C(n)): # Peter Luschny, Oct 06 2011

a(n) = denominator(n(n+1)/binomial(2n, n)).
a(n) = denominator(n/C(n)). - Paul Barry, Nov 17 2004
a(n) = C(n) / gcd(n, C(n)). - Peter Luschny, Oct 06 2011

A098510 Row sums of a matrix associated to the inverse of a Catalan scaled binomial matrix.

Original entry on oeis.org

1, 2, 5, 20, 49, 210, 429, 2860, 7293, 34034, 113373, 537472, 1359507, 6611810, 24627135, 37917616, 177181213, 973514514, 1647439975, 12026570280, 17818756259, 98555142278, 502860886675, 4577646742140, 6402665244089

Offset: 0

Paul Barry, Sep 11 2004

Row sums of A098509.

a(n)=sum{k=0..n, denominator((n+1)binomial(n, k)/binomial(2n, n))}

A098511 Diagonal sums of a matrix associated to the inverse of a Catalan scaled binomial matrix.

Original entry on oeis.org

1, 1, 3, 6, 21, 54, 186, 479, 1938, 5795, 22888, 70781, 286443, 861463, 3592105, 11492256, 39274353, 148852401, 613876868, 1917516257, 8511689170, 25445125513, 100975365920, 390096404027, 1666653892303, 5319341488465

Offset: 0

Paul Barry, Sep 11 2004

Diagonal sums of A098509.

a(n)=sum{k=0..floor(n/2), denominator((n-k+1)Binomial(n-k, k)/Binomial(2(n-k), n-k))}

cp's OEIS Frontend

A098512 Second column and subdiagonal of number triangle A098509.

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A098510 Row sums of a matrix associated to the inverse of a Catalan scaled binomial matrix.

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A098511 Diagonal sums of a matrix associated to the inverse of a Catalan scaled binomial matrix.

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Author

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