A235501 Riordan array (1/(1-2*x^2), x/(1-x)).

1, 0, 1, 2, 1, 1, 0, 3, 2, 1, 4, 3, 5, 3, 1, 0, 7, 8, 8, 4, 1, 8, 7, 15, 16, 12, 5, 1, 0, 15, 22, 31, 28, 17, 6, 1, 16, 15, 37, 53, 59, 45, 23, 7, 1, 0, 31, 52, 90, 112, 104, 68, 30, 8, 1, 32, 31, 83, 142, 202, 216, 172, 98, 38, 9, 1, 0, 63, 114, 225

Offset

0,4

Comments

Row sums are A007179(n+1).

Links

Table of n, a(n) for n=0..69.

Formula

T(n,n)=1, T(2n,0)=2^n, T(2n+1,0)=0, T(n,k)=T(n-1,k-1)+T(n-1,k) for 0<k<n.

T(n,k)=T(n-1,k)+T(n-1,k-1)+2*T(n-2,k)-T(n-3,k)-2*T(n-3,k-1), T(0,0)=1, T(1,0)=0, T(1,1)=1, T(n,k)=0 if k<0 or if k>n.

T(n,n)=1, T(n+1,n)=n, T(n+2,n)=n*(n+1)/2 + 2.

exp(x) * e.g.f. for row n = e.g.f. for diagonal n. For example, for n = 3 we have exp(x)*(3*x + 2*x^2/2! + x^3/3!) = 3*x + 8*x^2/2! + 16*x^3/3! + 28*x^4/4! + 45*x^5/5! + .... The same property holds more generally for Riordan arrays of the form ( f(x), x/(1 - x) ). - Peter Bala, Dec 22 2014

Example

Triangle begins (0<=k<=n):
1
0, 1
2, 1, 1
0, 3, 2, 1
4, 3, 5, 3, 1
0, 7, 8, 8, 4, 1
8, 7, 15, 16, 12, 5, 1
0, 15, 22, 31, 28, 17, 6, 1

Crossrefs

Cf. Columns: A077957, A052551, A077866.

Diagonals: A000012, A001477, A022856.

Cf. Similar sequences: A059260, A191582.

Sequence in context: A029340 A288166 A126258 * A116382 A050606 A352521

Adjacent sequences: A235498 A235499 A235500 * A235502 A235503 A235504

Keyword

nonn,easy,tabl

Author

Philippe Deléham, Jan 11 2014

Status

approved