OFFSET
0,2
COMMENTS
FORMULA
T(n, k) = n!*[x^k] p(n) where p(n) = [t^n] exp(3*t)*(1-t)^(-x).
EXAMPLE
The triangle starts:
{1}
{3, 1}
{9, 7, 1}
{27, 38, 12, 1}
{81, 192, 101, 18, 1}
{243, 969, 755, 215, 25, 1}
{729, 5115, 5494, 2205, 400, 33, 1}
{2187, 29322, 40971, 21469, 5355, 679, 42, 1}
{6561, 187992, 323658, 209356, 66619, 11452, 1078, 52, 1}
{19683, 1370745, 2764926, 2111318, 813645, 176295, 22302, 1626, 63, 1}
MAPLE
egf := exp(3*t)*(1-t)^(-x): ser := series(egf, t, 12): p := n -> coeff(ser, t, n):
seq(print(n!*seq(coeff(p(n), x, k), k=0..n)), n=0..9);
MATHEMATICA
p [n_] := HypergeometricU[-n, 1 - n - x, 3];
Table[CoefficientList[p[n], x], {n, 0, 9}] // Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Oct 27 2019
STATUS
approved