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A193977 Triangular array:  the fission of (p(n,x)) by (q(n,x)), where p(n,x)=x*p(n-1,x)+n+1 with p(0,x)=1, and q(n,x)=sum{(k+1)*x^k ; 0<=k<=n}. 3
2, 6, 5, 12, 14, 9, 20, 27, 24, 14, 30, 44, 45, 36, 20, 42, 65, 72, 66, 50, 27, 56, 90, 105, 104, 90, 66, 35, 72, 119, 144, 150, 140, 117, 84, 44, 90, 152, 189, 204, 200, 180, 147, 104, 54, 110, 189, 240, 266, 270, 255, 224, 180, 126, 65, 132, 230, 297, 336 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

LINKS

Table of n, a(n) for n=0..58.

EXAMPLE

First six rows:

2

6....5

12...14...9

20...27...24...14

30...44...45...36...20

42...65...72...66...50...27

MATHEMATICA

z = 11;

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

q[n_, x_] := Sum[(k + 1)*x^k, {k, 0, n}]

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

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

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

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

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

Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A193977 *)

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

Flatten[Table[h[n], {n, -1, z}]]  (* A193978 *)

CROSSREFS

Cf. A193842, A193978.

Sequence in context: A077174 A211201 A179627 * A092313 A318358 A230383

Adjacent sequences:  A193974 A193975 A193976 * A193978 A193979 A193980

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 10 2011

STATUS

approved

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Last modified November 28 00:12 EST 2021. Contains 349395 sequences. (Running on oeis4.)