A201093 Triangle T(n,k), read by rows, given by (0,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,...) DELTA (1,0,0,0,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938.

1, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 1, 1, 3, 1, 0, 0, 2, 3, 4, 1, 0, 2, 2, 4, 6, 5, 1, 0, 0, 4, 6, 8, 10, 6, 1, 0, 5, 5, 9, 13, 15, 15, 7, 1, 0, 0, 10, 15, 20, 25, 26, 21, 8, 1, 0, 14, 14, 24, 34, 41, 45, 42, 28, 9, 1

Offset

0,9

Comments

Riordan array (1,xf(x)) where f(x) is g.f. of A097331.

Row sums are in A001405.

Links

Table of n, a(n) for n=0..65.

Formula

Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A001405(n), A098617(n) for x = 0,1,2 respectively.

Example

Triangle begins :
1
0, 1
0, 1, 1
0, 0, 2, 1
0, 1, 1, 3, 1
0, 0, 2, 3, 4, 1
0, 2, 2, 4, 6, 5, 1
0, 0, 4, 6, 8, 10, 6, 1
0, 5, 5, 9, 13, 15, 15, 7, 1
0, 0, 10, 15, 20, 25, 26, 21, 8, 1
0, 14, 14, 24, 34, 41, 45, 42, 28, 9, 1
0, 0, 28, 42, 56, 70, 78, 77, 64, 36, 10, 1
0, 42, 42, 70, 98, 120, 136, 140, 126, 93, 45, 11, 1

Crossrefs

Cf. Diagonals : A000012, A001477, A000217, A000215,

Columns :A000007, A097331, A089408

Sequence in context: A294220 A214015 A137560 * A131255 A344566 A198295

Adjacent sequences: A201090 A201091 A201092 * A201094 A201095 A201096

Keyword

nonn,tabl

Author

Philippe Deléham, Nov 26 2011

Status

approved