A202847 Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A126930.

1, -1, 1, 2, -2, 1, -3, 5, -3, 1, 6, -10, 9, -4, 1, -10, 22, -22, 14, -5, 1, 20, -44, 54, -40, 20, -6, 1, -35, 93, -123, 109, -65, 27, -7, 1, 70, -186, 281, -276, 195, -98, 35, -8, 1, -126, 386, -618, 682, -541, 321, -140, 44, -9, 1

Offset

0,4

Links

Table of n, a(n) for n=0..54.

Formula

T(n,k) = (-1)^(n-k)*A054336(n,k).

Sum_{k, 0<=k<=n}T(n,k)*x^k = (-1)^n*A126931(n), (-1)^n*A054341(n), A126930(n), A126120(n), A001405(n), A054341(n), A126931(n) for x = -2, -1, 0, 1, 2, 3, 4 respectively.

Example

Triangle begins
1
-1, 1
2, -2, 1
-3, 5, -3, 1
6, -10, 9, -4, 1
-10, 22, -22, 14, -5, 1
20, -44, 54, -40, 20, -6, 1
-35, 93, -123, 109, -65, 27, -7, 1
...
Production matrix begins
x, 1
1, x, 1
1, 1, x, 1
1, 1, 1, x, 1
1, 1, 1, 1, x, 1
1, 1, 1, 1, 1, x, 1
1, 1, 1, 1, 1, 1, x, 1
1, 1, 1, 1, 1, 1, 1, x, 1
1, 1, 1, 1, 1, 1, 1, 1, x, 1
1, 1, 1, 1, 1, 1, 1, 1, 1, x, 1
..., with x = -1.

Crossrefs

Cf. (sequences with similar production matrix) A097609 (x=0), A033184 (x=1), A104259 (x=2), A171568 (x=3), A171589 (x=4)

Sequence in context: A182810 A139375 A106198 * A054336 A342908 A284644

Adjacent sequences: A202844 A202845 A202846 * A202848 A202849 A202850

Keyword

sign,tabl

Author

Philippe Deléham, Mar 02 2013

Status

approved