login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A154985 Polynomial recursion:m=1; p(x,n)=(x + 1)*p(x, n - 1) + 2^(m + n - 1)*x*p(x, n - 2)+If[n >= 3, 2^(n - 2)*x*p(x, n - 2), 0]. 0

%I

%S 1,1,1,1,6,1,1,17,17,1,1,38,154,38,1,1,79,872,872,79,1,1,160,3991,

%T 14064,3991,160,1,1,321,16791,157575,157575,16791,321,1,1,642,68312,

%U 1451486,4815630,1451486,68312,642,1,1,1283,274394,12266038,107115116,107115116

%N Polynomial recursion:m=1; p(x,n)=(x + 1)*p(x, n - 1) + 2^(m + n - 1)*x*p(x, n - 2)+If[n >= 3, 2^(n - 2)*x*p(x, n - 2), 0].

%C Row sums are:

%C {1, 2, 8, 36, 232, 1904, 22368, 349376, 7856512, 239313664, 10534962688,...}.

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

%F +If[n >= 3, 2^(n - 2)*x*p(x, n - 2), 0];

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

%e {1},

%e {1, 1},

%e {1, 6, 1},

%e {1, 17, 17, 1},

%e {1, 38, 154, 38, 1},

%e {1, 79, 872, 872, 79, 1},

%e {1, 160, 3991, 14064, 3991, 160, 1},

%e {1, 321, 16791, 157575, 157575, 16791, 321, 1},

%e {1, 642, 68312, 1451486, 4815630, 1451486, 68312, 642, 1},

%e {1, 1283, 274394, 12266038, 107115116, 107115116, 12266038, 274394, 1283, 1},

%e {1, 2564, 1097437, 99979792, 1977283234, 6378236632, 1977283234, 99979792, 1097437, 2564, 1}

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

%t p[x, n] = (x + 1)*p[ x, n - 1] + 2^(m + n - 1)*x*p[x, n - 2]

%t + If[n >= 3, 2^(n - 2)*x*p[x, n - 2], 0];

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

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

%t Flatten[%]

%K nonn,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Jan 18 2009

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 August 10 14:50 EDT 2020. Contains 336381 sequences. (Running on oeis4.)