login
A193630
Augmentation of the triangle A074909. See Comments.
1
1, 1, 2, 1, 5, 7, 1, 9, 28, 33, 1, 14, 74, 181, 191, 1, 20, 159, 637, 1333, 1297, 1, 27, 300, 1767, 5906, 11029, 10063, 1, 35, 517, 4190, 20256, 59324, 101351, 87669, 1, 44, 833, 8873, 58339, 244125, 645146, 1024949, 847015, 1, 54, 1274, 17241, 147680
OFFSET
0,3
COMMENTS
For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091.
Regarding A193630, writing the general term as w(n,k),
w(n,n): A104981
w(n,n-1): A156629
EXAMPLE
First five rows of A193607:
1
1...2
1...5....7
1...9....28...33
1...14...74...181...191
MATHEMATICA
p[n_, k_] := Binomial[n + 1, k];
Table[p[n, k], {n, 0, 7}, {k, 0, n}] (* A074909 *)
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}]] (* A193630 *)
Flatten[Table[v[n], {n, 0, 8}]]
CROSSREFS
Sequence in context: A143892 A129321 A064642 * A144505 A369527 A370382
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 01 2011
STATUS
approved