A086872 - OEIS

A086872

Triangle T(n, k) read by rows; given by [1, 2, 3, 4, 5, 6, ..] DELTA [1, 4, 9, 16, 25, 36, ...] where DELTA is the operator defined in A084938.

1, 1, 1, 3, 8, 5, 15, 75, 121, 61, 105, 840, 2478, 3128, 1385, 945, 11025, 51030, 115350, 124921, 50521, 10395, 166320, 1105335, 3859680, 7365633, 7158128, 2702765

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OFFSET

0,4

LINKS

Alois P. Heinz, Rows n = 0..140, flattened

FORMULA

Sum( k>=0, T(n, k)*(-1)^k ) = 0; if n>0.

Sum( k>=0, T(n, k)*(-1/2)^k ) = (1/2)^n.

Sum_{k, 0<=k<=n}T(n,k)*x^(n-k) = (-1)^n*A121822(n), (-1)^n*A092812(n), (-1)^n*A054879(n), A009117(n), A033999(n), A000007(n), A000364(n), A000182(n+1) for x = -6, -5, -4, -3, -2, -1, 0, 1 respectively .

EXAMPLE

Triangle begins:

1, 1;

3, 8, 5;

15, 75, 121, 61;

105, 840, 2478, 3128, 1385;

945, 11025, 51030, 115350, 124921, 50521;

10395, 166320, 1105335, 3859680, 7365633, 7158128, 2702765 ; ...

CROSSREFS

Cf. A000182 (row sums), A000364 (first diagonal), A001147 (first column), A084938, A261065 (2nd column).

Sequence in context: A120070 A143753 A121164 * A363421 A323760 A054792

Adjacent sequences: A086869 A086870 A086871 * A086873 A086874 A086875

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Aug 20 2003, Aug 17 2007

STATUS

approved