A097207 - OEIS

%I #18 Jul 26 2015 10:14:10

%S 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,

%T 9,35,77,105,91,49,15,1,10,44,112,182,196,140,64,17,1,11,54,156,294,

%U 378,336,204,81,19,1,12,65,210,450,672,714,540,285,100,21,1,13,77,275,660

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

%H Reinhard Zumkeller, <a href="/A097207/b097207.txt">Rows n=0..150 of triangle, flattened</a>

%H H. W. Gould, <a href="http://dx.doi.org/10.1137/0117030">Power sum identities for arbitrary symmetric arrays</a>, SIAM J. Appl. Math., 17 (1969), 307-316.

%H <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>

%F T(n,k) = A029635(n+1,k), 0 <= k <= n. - _Reinhard Zumkeller_, Mar 12 2012

%e Triangle begins:

%e 1

%e 1 3

%e 1 4 5

%e 1 5 9 7

%e 1 6 14 16 9

%t 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 *)

%o (Haskell)

%o a097207 n k = a097207_tabl !! n !! k

%o a097207_row n = a097207_tabl !! n

%o a097207_tabl = map init $ tail a029635_tabl

%o -- _Reinhard Zumkeller_, Mar 12 2012

%Y Cf. A029637, A110813 (row-reversed).

%K nonn,tabl,easy

%O 0,3

%A _N. J. A. Sloane_, Sep 21 2004

%E More terms from _Robert G. Wilson v_, Sep 21 2004