A059328 - OEIS

%I #12 Jan 07 2017 17:10:35

%S 1,1,1,1,3,1,1,7,7,1,1,15,63,15,1,1,31,1023,1023,31,1,1,63,32767,

%T 1048575,32767,63,1,1,127,2097151,34359738367,34359738367,2097151,127,

%U 1,1,255,268435455,72057594037927935,1180591620717411303423

%N Table T(n,k) = T(n - 1,k) + T(n,k - 1) + T(n - 1,k)*T(n,k - 1) starting with T(0,0)=1, read by antidiagonals.

%C In binary representation T(n,k) is the concatenation of T(n-1,k-1) and T(n-1,k), 0<k<n. - _Reinhard Zumkeller_, Jan 23 2003

%H G. C. Greubel, <a href="/A059328/b059328.txt">Table of n, a(n) for the first 14 rows, flattened</a>

%F T(n, k) = 2^C(n+k, n)-1; a(n) = 2^A007318(n)-1.

%F If U(n, k) := 1 + T(n, k), then U(n, k) = U(n-1, k) * U(n, k-1). - _Michael Somos_, Jan 07 2017

%t Table[2^(Binomial[n, k]) - 1, {n, 0, 5}, {k, 0, n}] (* _G. C. Greubel_, Jan 07 2017 *)

%Y Cf. A007318.

%K nonn,tabl

%O 0,5

%A _Henry Bottomley_, Jan 26 2001