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A137153
Triangle, read by rows, where T(n,k) = C(2^k + n-k-1, n-k).
6
1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 10, 8, 1, 1, 5, 20, 36, 16, 1, 1, 6, 35, 120, 136, 32, 1, 1, 7, 56, 330, 816, 528, 64, 1, 1, 8, 84, 792, 3876, 5984, 2080, 128, 1, 1, 9, 120, 1716, 15504, 52360, 45760, 8256, 256, 1, 1, 10, 165, 3432, 54264, 376992, 766480, 357760, 32896
OFFSET
0,5
COMMENTS
Matrix inverse is A137156.
EXAMPLE
Triangle begins:
1;
1, 1;
1, 2, 1;
1, 3, 4, 1;
1, 4, 10, 8, 1;
1, 5, 20, 36, 16, 1;
1, 6, 35, 120, 136, 32, 1;
1, 7, 56, 330, 816, 528, 64, 1;
1, 8, 84, 792, 3876, 5984, 2080, 128, 1;
1, 9, 120, 1716, 15504, 52360, 45760, 8256, 256, 1;
1, 10, 165, 3432, 54264, 376992, 766480, 357760, 32896, 512, 1;
...
MATHEMATICA
Table[Binomial[2^k+n-k-1, n-k], {n, 0, 10}, {k, 0, n}]//Flatten (* Harvey P. Dale, Mar 06 2017 *)
PROG
(PARI) {T(n, k)=binomial(2^k+n-k-1, n-k)}
for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))
(PARI) {T(n, k) = polcoeff(1/(1-x+x*O(x^n))^(2^k), n-k)}
for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))
CROSSREFS
Cf. A137154 (row sums), A137155 (antidiagonal sums), A060690 (central terms); A137156 (matrix inverse).
Cf. A092056 (same with reflected rows).
Sequence in context: A162717 A122175 A073165 * A340814 A063841 A256161
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Jan 24 2008
STATUS
approved