OFFSET
0,4
FORMULA
T(n, k) = (2*n)! [x^k] [y^(2*n)] sec(y*sqrt(x - 1)).
Sum_{k=0..n} (-1)^(n-k)*T(n, k) = |A012816(n+1)|.
EXAMPLE
Triangle starts:
[0] 1;
[1] -1, 1;
[2] 5, -10, 5;
[3] -61, 183, -183, 61;
[4] 1385, -5540, 8310, -5540, 1385;
[5] -50521, 252605, -505210, 505210, -252605, 50521;
[6] 2702765, -16216590, 40541475, -54055300, 40541475, -16216590, 2702765;
MATHEMATICA
gf := Sec[y Sqrt[x - 1]]; ser := Series[gf, {y, 0, 26}];
cy[n_] := n! Coefficient[ser, y, n]; row[n_] := CoefficientList[cy[2 n], x];
Table[row[n], {n, 0, 7}] // Flatten
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Peter Luschny, Aug 06 2019
STATUS
approved