OFFSET
0,4
FORMULA
T(n, k) = (2*n-1)! [x^k] [y^(2*n-1)] sqrt(x - 1)*tan(y*sqrt(x - 1)) for n > 0.
Sum_{k=0..n} (-1)^(n-k)*T(n, k) = 2*A261042(n-1) for n > 0.
EXAMPLE
Triangle starts:
[0] 0;
[1] -1, 1;
[2] 2, -4, 2;
[3] -16, 48, -48, 16;
[4] 272, -1088, 1632, -1088, 272;
[5] -7936, 39680, -79360, 79360, -39680, 7936;
[6] 353792, -2122752, 5306880, -7075840, 5306880, -2122752, 353792;
MAPLE
T := (n, k) -> (-1)^(n - k)*binomial(n, k)*A000182(n):
seq(seq(T(n, k), k = 0..n), n = 0..6); # Peter Luschny, Apr 23 2024
MATHEMATICA
gf := Sqrt[x - 1] Tan[y Sqrt[x - 1]];
ser := Series[gf, {y, 0, 26}];
cy[n_] := n! Coefficient[ser, y, n];
row[n_] := If[n == 0, 0, CoefficientList[cy[2 n - 1], x]];
Table[row[n], {n, 0, 7}] // Flatten
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Peter Luschny, Aug 08 2019
EXTENSIONS
Offset set to 0, T(0,0) = 0 and new name by Peter Luschny, Apr 23 2024
STATUS
approved