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A193971 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)=(x+1)^n. 2
2, 3, 5, 4, 11, 9, 5, 19, 26, 14, 6, 29, 55, 50, 20, 7, 41, 99, 125, 85, 27, 8, 55, 161, 259, 245, 133, 35, 9, 71, 244, 476, 574, 434, 196, 44, 10, 89, 351, 804, 1176, 1134, 714, 276, 54, 11, 109, 485, 1275, 2190, 2562, 2058, 1110, 375, 65, 12, 131, 649, 1925 (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

3...5

4...11....9

5...19...26...14

6...29...55...50...20

7...41...99...125..85...27

MAPLE

# The function 'fission' is defined in A193842.

p := (n, x) -> `if`(n=0, 1, x*p(n-1, x)+n+1);

q := (n, x) -> (x+1)^n;

A193971_row := n -> fission(p, q, n);

for n from 0 to 5 do A193971_row(n) od; # Peter Luschny, Jul 23 2014

MATHEMATICA

z = 11;

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

q[n_, x_] := (x + 1)^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}]]  (* A193971 *)

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

Flatten[Table[h[n], {n, -1, z}]]  (* A193972 *)

PROG

(Sage) # uses[fission from A193842]

p = lambda n, x: x*p(n-1, x)+n+1 if n > 0 else 1

q = lambda n, x: (x+1)^n

A193971_row = lambda n: fission(p, q, n);

for n in range(7): A193971_row(n) # Peter Luschny, Jul 23 2014

CROSSREFS

Cf. A193842, A193972.

Sequence in context: A213900 A213648 A302849 * A258861 A171038 A023395

Adjacent sequences:  A193968 A193969 A193970 * A193972 A193973 A193974

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 10 2011

STATUS

approved

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Last modified April 18 22:45 EDT 2021. Contains 343098 sequences. (Running on oeis4.)