A136205 Square array read by antidiagonals: T(m,n) = H(n,2*m)*(2*m)!/(2*m+2*n-1). H(0,m) = 1/m, for all positive integers m. H(n,m) = Sum_{k=1..m} H(n-1,k).

1, 1, 2, 1, 10, 24, 1, 22, 252, 720, 1, 38, 892, 12176, 40320, 1, 58, 2232, 60336, 966240, 3628800, 1, 82, 4632, 199440, 6202080, 114341760, 479001600, 1, 110, 8524, 526256, 25598016, 905049216, 18897709824, 87178291200, 1, 142, 14412, 1197360

Offset: 0

Author

Leroy Quet, Mar 16 2008

Keywords

• nonn
• tabl

Comments

In the array, the first m is 1; the first n is 0.

Every term of the array is a positive integer.

Examples

			Array: (The upper-leftmost term is T(1,0).)
  1, 2, 24, 720 (Row equals {(2*m-2)!}.)
  1, 10, 252 (Row equals {H(1,2*m)*(2*m)!/(2*m+1)}, where H(1,2*m) = the (2*m)th harmonic number.)
  1, 22 (Row equals {H(2,2*m)*(2*m)!/(2*m+3)}.)
  1 (Row equals {H(3,2*m)*(2*m)!/(2*m+5)}.)
The column {T(1,n)} consists entirely of 1's.
		

Crossrefs

Cf. A105954.

Cf. A090288, A010050, A114450.

Formula

For n>=1, T(m,n) also equals (H(2*m+n-1) - H(n-1)) * (2*m+n-1)!/((2*m+2*n-1)*(n-1)!), where H(k) = H(1,k), the k-th harmonic number.

Extensions

More terms from R. J. Mathar, Apr 01 2008