A114449 - OEIS

%I #15 Nov 14 2024 10:23:01

%S 1,22,2232,526256,223342560,149004576000,143638792012800,

%T 188865721926604800,324805825447366348800,707653302810219988992000,

%U 1904745046396912124461056000,6206775274489558456631623680000

%N 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).

%C Every term is an integer.

%e H(2,4) = H(1,1) +H(1,2) +H(1,3) +H(1,4) =

%e 1 + (1 +1/2) + (1 +1/2 +1/3) + (1 +1/2 + 1/3 +1/4) = 77/12.

%e So a(2) = 24 *(77/12)/7 = 22.

%p 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

%t H[0, n_] := 1/n;

%t H[m_, n_] := H[m, n] = Sum[H[m-1, k], {k, 1, n}];

%t a[n_] := (2n)! H[n, 2n]/(4n-1);

%t Table[a[n], {n, 1, 12}] (* _Jean-François Alcover_, Nov 14 2024 *)

%K nonn

%O 1,2

%A _Leroy Quet_, Feb 14 2006

%E More terms from _Brent A. Yorgey_, Jul 27 2007

%E More terms from _R. J. Mathar_, Jan 30 2008