login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A154979 Polynomial recursion:m=2; p(x,n)=(x + 1)*p(x, n - 1) + 2^(m + n - 1)*x*p(x, n - 2). 0
1, 1, 1, 1, 10, 1, 1, 27, 27, 1, 1, 60, 374, 60, 1, 1, 125, 2162, 2162, 125, 1, 1, 254, 9967, 52196, 9967, 254, 1, 1, 511, 42221, 615635, 615635, 42221, 511, 1, 1, 1024, 172780, 5760960, 27955622, 5760960, 172780, 1024, 1, 1, 2049, 697068, 49168044 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 12, 56, 496, 4576, 72640, 1316736, 39825152, 1427987968, 84417887232,...}.

LINKS

Table of n, a(n) for n=0..48.

FORMULA

m=2; p(x,n)=(x + 1)*p(x, n - 1) + 2^(m + n - 1)*x*p(x, n - 2);

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

EXAMPLE

{1},

{1, 1},

{1, 10, 1},

{1, 27, 27, 1},

{1, 60, 374, 60, 1}, {1, 125, 2162, 2162, 125, 1}, {1, 254, 9967, 52196, 9967, 254, 1},

{1, 511, 42221, 615635, 615635, 42221, 511, 1},

{1, 1024, 172780, 5760960, 27955622, 5760960, 172780, 1024, 1},

{1, 2049, 697068, 49168044, 664126822, 664126822, 49168044, 697068, 2049, 1},

{1, 4098, 2796269, 403718552, 12511740946, 58581367500, 12511740946, 403718552, 2796269, 4098, 1}

MATHEMATICA

Clear[p, n, m, x]; m = 2; p[x, 0] = 1; p[x, 1] = x + 1;

p[x_, n_] := p[x, n] = (x + 1)*p[x, n - 1] + 2^(m + n - 1)*x*p[x, n - 2];

Table[ExpandAll[p[x, n]], {n, 0, 10}];

Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A166341 A113280 A159041 * A146765 A190152 A154984

Adjacent sequences:  A154976 A154977 A154978 * A154980 A154981 A154982

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Jan 18 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 25 15:15 EDT 2019. Contains 323568 sequences. (Running on oeis4.)