A156960 q-Carlitz-Al-Salam-Appell polynomial coefficients:q=2; p(x,n)=x*p[x, n - 1] - (1 - q^(n - 1))*q^(n - 2)*p[x, n - 2].

1, 0, 1, 1, 0, 1, 0, 7, 0, 1, 28, 0, 35, 0, 1, 0, 868, 0, 155, 0, 1, 13888, 0, 18228, 0, 651, 0, 1, 0, 1763776, 0, 330708, 0, 2667, 0, 1, 112881664, 0, 149920960, 0, 5622036, 0, 10795, 0, 1, 0, 57682530304, 0, 10944230080, 0, 92672916, 0, 43435, 0, 1

Offset

0,8

Comments

Row sums are:

{1, 1, 2, 8, 64, 1024, 32768, 2097152, 268435456, 68719476736, 35184372088832,...}.

References

T Ernst,The different tongues of q - calculus,Proceedings of the Estonian Academy of Sciences, 2008 - kirj.ee, 2-81-99,pp.14-15

Links

Table of n, a(n) for n=0..54.

Formula

q=2; p(x,n)=x*p[x, n - 1] - (1 - q^(n - 1))*q^(n - 2)*p[x, n - 2];

t(n,m)=coefficients(p(x,n)).

Example

{1},
{0, 1},
{1, 0, 1},
{0, 7, 0, 1},
{28, 0, 35, 0, 1},
{0, 868, 0, 155, 0, 1},
{13888, 0, 18228, 0, 651, 0, 1},
{0, 1763776, 0, 330708, 0, 2667, 0, 1},
{112881664, 0, 149920960, 0, 5622036, 0, 10795, 0, 1},
{0, 57682530304, 0, 10944230080, 0, 92672916, 0, 43435, 0, 1},
{14766727757824, 0, 19669742833664, 0, 746396491456, 0, 1504831636, 0, 174251, 0, 1}

Mathematica

Clear[p, x, n, q];
p[x, 0] := 1; p[x, 1] := x;
p[x_, n_] := p[x, n] = x*p[x, n - 1] - (1 - q^(n - 1))*q^(n - 2)*p[x, n - 2];
q = 2; Table[ExpandAll[p[x, n]], {n, 0, 10}];
Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A297787 A101031 A222063 * A287697 A335953 A227958

Adjacent sequences: A156957 A156958 A156959 * A156961 A156962 A156963

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Feb 19 2009

Status

approved