A112358 -id:A112358 - cp's OEIS frontend

A112359 Product of n-th row of A112358.

1, 2, 20, 1296, 616896, 2294480000, 68803020000000, 16921170978243840000, 34496793424028349312532480, 587395062985562798532990766497792, 84034508984208959408391703340160000000000, 101510206136861741998326287566434701976960000000000

Offset: 0

Amarnath Murthy, Sep 05 2005

Cf. A112356, A112357, A112358.

A008949 := proc(n,k) local i ; add(binomial(n,i),i=0..k) ; end: A112358 := proc(n,k) if k = 0 then 1 ; else binomial(n,k)*(A008949(n+1,k)+1)/2 ; fi ; end: A112359 := proc(n) local k ; mul( A112358(n,k),k=0..n ) ; end: for n from 0 to 15 do printf("%d, ",A112359(n)) ; od ; # R. J. Mathar, May 08 2007

A008949[n_, k_] := Sum[Binomial[n, j], {j, 0, k}];
A112358[n_, k_] := If[k == 0, 1, Binomial[A008949[n, k] + 1, 2] - Binomial[A008949[n, k - 1] + 1, 2]];
a[n_] := Product[A112358[n, k], {k, 0, n}];
Table[a[n], {n, 0, 11}] (* Jean-François Alcover, Aug 01 2023, after R. J. Mathar *)

More terms from R. J. Mathar, May 08 2007

A112360 Triangle read by rows: T(n,k) is the LCM of all C(n,k) integers from 1 + C(n,0) + C(n,1) + ... + C(n,k-1) to C(n,0) + C(n,1) + ... + C(n,k) (0 <= k <= n).

Original entry on oeis.org

1, 1, 2, 1, 6, 4, 1, 12, 210, 8, 1, 60, 27720, 5460, 16, 1, 60, 720720, 13385572200, 3398220, 32, 1, 420, 232792560, 219060189739591200, 60218289392461200, 4076731260, 64, 1, 840, 2329089562800, 1182266884102822267511361600

Offset: 0

Amarnath Murthy, Sep 07 2005

Column 1 yields A003418. a(n,n) = 2^n. - Emeric Deutsch, Feb 03 2006

			Triangle begins:
  1;
  1,  2;
  1,  6,     4;
  1, 12,   210,    8;
  1, 60, 27720, 5460, 16;
  ...
The row for n = 3 is
1....3..........3.......1
1 lcm(2*3*4) lcm(5*6*7) 8 ====> 1 12 210 8.

Cf. A112356, A112357, A112358, A112359.

T:=proc(n,k) if n=0 and k=0 then 1 else lcm(seq(j,j=1+sum(binomial(n,i),i=0..k-1)..sum(binomial(n,i),i=0..k))) fi end: for n from 0 to 7 do seq(T(n,k),k=0..n) od; # yields sequence in triangular form - Emeric Deutsch, Feb 03 2006

More terms from Emeric Deutsch, Feb 03 2006

cp's OEIS Frontend

A112359 Product of n-th row of A112358.

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