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A085707
Triangular array A065547 unsigned and transposed.
4
1, 1, 0, 1, 1, 0, 1, 3, 3, 0, 1, 6, 17, 17, 0, 1, 10, 55, 155, 155, 0, 1, 15, 135, 736, 2073, 2073, 0, 1, 21, 280, 2492, 13573, 38227, 38227, 0, 1, 28, 518, 6818, 60605, 330058, 929569, 929569, 0, 1, 36, 882, 16086, 211419, 1879038, 10233219, 28820619
OFFSET
0,8
REFERENCES
Louis Comtet, Analyse Combinatoire, PUF, 1970, Tome 2, pp. 98-99.
LINKS
J. M. Hammersley, An undergraduate exercise in manipulation, Math. Scientist, 14 (1989), 1-23. (Annotated scanned copy)
J. M. Hammersley, An undergraduate exercise in manipulation, Math. Scientist, 14 (1989), 1-23.
FORMULA
Sum_{k >= 0} (-1/2)^k*T(n, k) = (1/2)^n.
Sum_{k >= 0} (-1/6)^k*T(n, k) = (4^(n+1)- 1)/3*(6^n).
Equals A000035 DELTA [0, 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, ...], where DELTA is Deléham's operator defined in A084938.
T(n,n-1) = A110501(n), Genocchi numbers of first kind of even index. - Philippe Deléham, Feb 16 2007
EXAMPLE
1;
1, 0;
1, 1, 0;
1, 3, 3, 0;
1, 6, 17, 17, 0;
1, 10, 55, 155, 155, 0;
...
MATHEMATICA
h[n_, x_] := Sum[c[k]*x^k, {k, 0, n}]; eq[n_] := SolveAlways[h[n, x*(x-1)] == EulerE[2*n, x], x]; row[n_] := Table[c[k], {k, 0, n}] /. eq[n] // First // Abs // Reverse; Table[row[n], {n, 0, 10}] // Flatten (* Jean-François Alcover, Oct 02 2013 *)
CROSSREFS
Row sums Sum_{k>=0} T(n, k) = A006846(n), values of Hammersley's polynomial p_n(1).
Sum_{k>=0} 2^k*T(n, k) = A005647(n), Salie numbers.
Sum_{k>=0} 3^k*T(n, k) = A094408(n).
Sum_{k>=0} 4^k*T(n, k) = A000364(n), Euler numbers.
Sequence in context: A193470 A102752 A104548 * A320253 A141947 A216804
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Jul 19 2003
STATUS
approved