

A193591


Augmentation of the Euler partition triangle A026820. See Comments.


1



1, 1, 2, 1, 4, 7, 1, 7, 19, 31, 1, 10, 45, 103, 161, 1, 14, 82, 297, 617, 937, 1, 18, 146, 652, 2057, 4005, 5953, 1, 23, 228, 1395, 5251, 15004, 27836, 40668, 1, 28, 355, 2555, 13023, 43470, 115110, 205516, 295922, 1, 34, 509, 4689, 27327, 122006, 371942
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OFFSET

0,3


COMMENTS

For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091.
Regarding A193591, column 1)=A014616.


LINKS

Table of n, a(n) for n=0..51.


EXAMPLE

First 5 rows of A193589:
1
1...2
1...4...7
1...7...19...31
1...10..45...103...161


MATHEMATICA

p[n_, k_] := Length@IntegerPartitions[n + 1,
k + 1] (* A026820, Euler partition triangle *)
Table[p[n, k], {n, 0, 5}, {k, 0, n}]
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, 12}]] (* A193591 *)
Flatten[Table[v[n], {n, 0, 9}]]


CROSSREFS

Cf. A026820, A193091.
Sequence in context: A193589 A187115 A121722 * A218842 A219421 A297314
Adjacent sequences: A193588 A193589 A193590 * A193592 A193593 A193594


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Jul 31 2011


STATUS

approved



