A097207 Triangle read by rows: T(n,k) = binomial(n,k) + 2*binomial(n,k-1).

1, 1, 3, 1, 4, 5, 1, 5, 9, 7, 1, 6, 14, 16, 9, 1, 7, 20, 30, 25, 11, 1, 8, 27, 50, 55, 36, 13, 1, 9, 35, 77, 105, 91, 49, 15, 1, 10, 44, 112, 182, 196, 140, 64, 17, 1, 11, 54, 156, 294, 378, 336, 204, 81, 19, 1, 12, 65, 210, 450, 672, 714, 540, 285, 100, 21, 1, 13, 77, 275, 660

Offset

0,3

Links

Reinhard Zumkeller, Rows n=0..150 of triangle, flattened

H. W. Gould, Power sum identities for arbitrary symmetric arrays, SIAM J. Appl. Math., 17 (1969), 307-316.

Index entries for triangles and arrays related to Pascal's triangle

Formula

T(n,k) = A029635(n+1,k), 0 <= k <= n. - Reinhard Zumkeller, Mar 12 2012

Example

Triangle begins:
1
1 3
1 4 5
1 5 9 7
1 6 14 16 9

Mathematica

T[n_, k_] := Binomial[n, k] + 2Binomial[n, k - 1]; Flatten[ Table[ T[n, k], {n, 0, 10}, {k, 0, n}]] (* Robert G. Wilson v, Sep 21 2004 *)

Prog

(Haskell)
a097207 n k = a097207_tabl !! n !! k
a097207_row n = a097207_tabl !! n
a097207_tabl = map init $ tail a029635_tabl
-- Reinhard Zumkeller, Mar 12 2012

Crossrefs

Cf. A029637, A110813 (row-reversed).

Sequence in context: A343516 A366977 A029637 * A266101 A118469 A319649

Adjacent sequences: A097204 A097205 A097206 * A097208 A097209 A097210

Keyword

nonn,tabl,easy

Author

N. J. A. Sloane, Sep 21 2004

Extensions

More terms from Robert G. Wilson v, Sep 21 2004

Status

approved