A114449 If H(0,n) = 1/n, H(m,n) = sum{k=1...n} H(m-1,k), then a(n) = (2n)!*H(n,2n)/(4n-1).

1, 22, 2232, 526256, 223342560, 149004576000, 143638792012800, 188865721926604800, 324805825447366348800, 707653302810219988992000, 1904745046396912124461056000, 6206775274489558456631623680000

Offset

1,2

Comments

Every term is an integer.

Links

Table of n, a(n) for n=1..12.

Example

H(2,4) = H(1,1) +H(1,2) +H(1,3) +H(1,4) =
1 + (1 +1/2) + (1 +1/2 +1/3) + (1 +1/2 + 1/3 +1/4) = 77/12.
So a(2) = 24 *(77/12)/7 = 22.

Maple

H := proc(m, n) option remember ; if m = 0 then 1/n ; else add( H(m-1, k), k=1..n) ; fi ; end: A114449 := proc(n) (2*n)!*H(n, 2*n)/(4*n-1) ; end: for n from 1 to 20 do printf("%d, ", A114449(n)) ; od: # R. J. Mathar, Jan 30 2008

Mathematica

H[0, n_] := 1/n;
H[m_, n_] := H[m, n] = Sum[H[m-1, k], {k, 1, n}];
a[n_] := (2n)! H[n, 2n]/(4n-1);
Table[a[n], {n, 1, 12}] (* Jean-François Alcover, Nov 14 2024 *)

Crossrefs

Sequence in context: A253128 A046445 A133235 * A069221 A069222 A117990

Adjacent sequences: A114446 A114447 A114448 * A114450 A114451 A114452

Keyword

nonn

Author

Leroy Quet, Feb 14 2006

Extensions

More terms from Brent A. Yorgey, Jul 27 2007

More terms from R. J. Mathar, Jan 30 2008

Status

approved