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A059328 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. 1
1, 1, 1, 1, 3, 1, 1, 7, 7, 1, 1, 15, 63, 15, 1, 1, 31, 1023, 1023, 31, 1, 1, 63, 32767, 1048575, 32767, 63, 1, 1, 127, 2097151, 34359738367, 34359738367, 2097151, 127, 1, 1, 255, 268435455, 72057594037927935, 1180591620717411303423 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

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

LINKS

G. C. Greubel, Table of n, a(n) for the first 14 rows, flattened

FORMULA

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

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

MATHEMATICA

Table[2^(Binomial[n, k]) - 1, {n, 0, 5}, {k, 0, n}] (* G. C. Greubel, Jan 07 2017 *)

CROSSREFS

Cf. A007318.

Sequence in context: A141689 A058669 A057004 * A174387 A176791 A259471

Adjacent sequences:  A059325 A059326 A059327 * A059329 A059330 A059331

KEYWORD

nonn,tabl

AUTHOR

Henry Bottomley, Jan 26 2001

STATUS

approved

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Last modified July 16 23:49 EDT 2019. Contains 325092 sequences. (Running on oeis4.)