A193093 Augmentation of the triangular array P=A094727 given by p(n,k)=n+k+1 for 0<=k<=n. See Comments.

1, 2, 3, 6, 14, 19, 24, 72, 130, 169, 120, 432, 918, 1482, 1877, 720, 3000, 7224, 13140, 19846, 24675, 5040, 23760, 63600, 127104, 210726, 304006, 372611, 40320, 211680, 622080, 1350000, 2412408, 3754656, 5234114, 6340961, 362880, 2096640

Offset

0,2

Comments

For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091.

Regarding W=A193093, we have w(n,0)=(n+1)! .

Links

Table of n, a(n) for n=0..37.

Example

First 5 rows:
1
2.....3
6.....14....19
24....72....130....169
120...432....918...1482...1877

Mathematica

p[n_, k_] := n + k + 1
Table[p[n, k], {n, 0, 5}, {k, 0, n}] (* A094727 *)
m[n_] := Table[If[i <= j, p[n + 1 - i, j - i], 0], {i, n}, {j, n + 1}]
TableForm[m[4]]
w[0, 0] = 1; w[1, 0] = p[1, 0]; w[1, 1] = p[1, 1];
v[0] = w[0, 0]; v[1] = {w[1, 0], w[1, 1]};
v[n_] := v[n - 1].m[n]
TableForm[Table[v[n], {n, 0, 6}]] (* A193093 *)
Flatten[Table[v[n], {n, 0, 8}]]

Crossrefs

Cf. A094727.

Sequence in context: A005537 A306600 A282351 * A182756 A152092 A187033

Adjacent sequences: A193090 A193091 A193092 * A193094 A193095 A193096

Keyword

nonn,tabl

Author

Clark Kimberling, Jul 30 2011

Status

approved