A238801 - OEIS

A238801

Triangle T(n,k), read by rows, given by T(n,k) = C(n+1, k+1)*(1-(k mod 2)).

1, 2, 0, 3, 0, 1, 4, 0, 4, 0, 5, 0, 10, 0, 1, 6, 0, 20, 0, 6, 0, 7, 0, 35, 0, 21, 0, 1, 8, 0, 56, 0, 56, 0, 8, 0, 9, 0, 84, 0, 126, 0, 36, 0, 1, 10, 0, 120, 0, 252, 0, 120, 0, 10, 0, 11, 0, 165, 0, 462, 0, 330, 0, 55, 0, 1, 12, 0, 220, 0, 792, 0, 792, 0, 220, 0, 12, 0

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OFFSET

0,2

COMMENTS

Row sums are powers of 2.

LINKS

G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened

FORMULA

G.f.: 1/((1+(y-1)*x)*(1-(y+1)*x)).

T(n,k) = 2*T(n-1,k) + T(n-2,k-2) - T(n-2,k), T(0,0) = 1, T(1,0) = 2, T(1,1) = 0, T(n,k) = 0 if k<0 or if k>n.

Sum_{k=0..n} T(n,k)*x^k = A000027(n+1), A000079(n), A015518(n+1), A003683(n+1), A079773(n+1), A051958(n+1), A080920(n+1), A053455(n), A160958(n+1) for x = 0, 1, 2, 3, 4, 5, 6, 7, 8 respectively.

EXAMPLE

Triangle begins:

2, 0;

3, 0, 1;

4, 0, 4, 0;

5, 0, 10, 0, 1;

6, 0, 20, 0, 6, 0;

7, 0, 35, 0, 21, 0, 1;

8, 0, 56, 0, 56, 0, 8, 0;

9, 0, 84, 0, 126, 0, 36, 0, 1;

10, 0, 120, 0, 252, 0, 120, 0, 10, 0; etc.

MATHEMATICA