A112359 - OEIS

%I #11 Aug 01 2023 07:48:53

%S 1,2,20,1296,616896,2294480000,68803020000000,16921170978243840000,

%T 34496793424028349312532480,587395062985562798532990766497792,

%U 84034508984208959408391703340160000000000,101510206136861741998326287566434701976960000000000

%N Product of n-th row of A112358.

%p 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

%t A008949[n_, k_] := Sum[Binomial[n, j], {j, 0, k}];

%t A112358[n_, k_] := If[k == 0, 1, Binomial[A008949[n, k] + 1, 2] - Binomial[A008949[n, k - 1] + 1, 2]];

%t a[n_] := Product[A112358[n, k], {k, 0, n}];

%t Table[a[n], {n, 0, 11}] (* _Jean-François Alcover_, Aug 01 2023, after _R. J. Mathar_ *)

%Y Cf. A112356, A112357, A112358.

%K easy,nonn

%O 0,2

%A _Amarnath Murthy_, Sep 05 2005

%E More terms from _R. J. Mathar_, May 08 2007