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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A193975 Triangular array:  the self-fission of (p(n,x)), where p(n,x)=x*p(n-1,x)+n+1, where p(0,x)=1. 2

%I

%S 2,3,8,4,11,20,5,14,26,40,6,17,32,50,70,7,20,38,60,85,112,8,23,44,70,

%T 100,133,168,9,26,50,80,115,154,196,240,10,29,56,90,130,175,224,276,

%U 330,11,32,62,100,145,196,252,312,375,440,12,35,68,110,160,217,280

%N Triangular array: the self-fission of (p(n,x)), where p(n,x)=x*p(n-1,x)+n+1, where p(0,x)=1.

%C See A193842 for the definition of fission of two sequences of polynomials or triangular arrays.

%e First six rows:

%e 2

%e 3...8

%e 4...11...20

%e 5...14...26...40

%e 6...17...32...50...70

%e 7...20...38...60...85...112

%t z = 11;

%t p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n + 1;

%t q[n_, x_] := p[n, x];

%t p1[n_, k_] := Coefficient[p[n, x], x^k];

%t p1[n_, 0] := p[n, x] /. x -> 0;

%t d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]

%t h[n_] := CoefficientList[d[n, x], {x}]

%t TableForm[Table[Reverse[h[n]], {n, 0, z}]]

%t Flatten[Table[Reverse[h[n]], {n, -1, z}]] (* A193975 *)

%t TableForm[Table[h[n], {n, 0, z}]]

%t Flatten[Table[h[n], {n, -1, z}]] (* A193976 *)

%Y Cf. A193842, A193976.

%K nonn,tabl

%O 0,1

%A _Clark Kimberling_, Aug 10 2011

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 December 2 12:01 EST 2021. Contains 349440 sequences. (Running on oeis4.)