|
| |
|
|
A108044
|
|
Triangle read by rows: right half of Pascal's triangle (A007318) interspersed with 0's.
|
|
6
| |
|
|
1, 0, 1, 2, 0, 1, 0, 3, 0, 1, 6, 0, 4, 0, 1, 0, 10, 0, 5, 0, 1, 20, 0, 15, 0, 6, 0, 1, 0, 35, 0, 21, 0, 7, 0, 1, 70, 0, 56, 0, 28, 0, 8, 0, 1, 0, 126, 0, 84, 0, 36, 0, 9, 0, 1, 252, 0, 210, 0, 120, 0, 45, 0, 10, 0, 1, 0, 462, 0, 330, 0, 165, 0, 55, 0, 11, 0, 1, 924, 0, 792, 0, 495, 0, 220, 0, 66
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
COMMENTS
| Column k has e.g.f. Bessel_I(k,2x). [From Paul Barry (pbarry(AT)wit.ie), Mar 10 2010]
|
|
|
REFERENCES
| L. W. Shapiro, S. Getu, W.-J. Woan and L. C. Woodson, The Riordan group, Discrete Applied Math., 34 (1991), 229-239.
|
|
|
FORMULA
| Each entry is the sum of those in the previous row that are to its left and to its right.
Riordan array (1/sqrt(1-4*x^2), (1-sqrt(1-4*x^2))/(2*x)).
T(n, k)=binomial(n, (n+k)/2) if n+k is even, T(n, k)=0 if n+k is odd. G.f.=f/(1-tg), where f=1/sqrt(1-4x^2) and g=(1-sqrt(1-4x^2))/(2x). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 05 2005
|
|
|
EXAMPLE
| Triangle begins:
.1
.0 1
.2 0 1
.0 3 0 1
.6 0 4 0 1
.0 10 0 5 0 1
.20 0 15 0 6 0 1
Contribution from Paul Barry (pbarry(AT)wit.ie), Mar 10 2010: (Start)
Production matrix is
0, 1,
2, 0, 1,
0, 1, 0, 1,
0, 0, 1, 0, 1,
0, 0, 0, 1, 0, 1,
0, 0, 0, 0, 1, 0, 1,
0, 0, 0, 0, 0, 1, 0, 1,
0, 0, 0, 0, 0, 0, 1, 0, 1,
0, 0, 0, 0, 0, 0, 0, 1, 0, 1 (End)
|
|
|
MAPLE
| T:=proc(n, k) if n+k mod 2 = 0 then binomial(n, (n+k)/2) else 0 fi end: for n from 0 to 13 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form (Deutsch)
|
|
|
CROSSREFS
| Cf. A007318, A108045.
Cf. A204293.
Sequence in context: A134511 A112554 A120616 * A104477 A052173 A175790
Adjacent sequences: A108041 A108042 A108043 * A108045 A108046 A108047
|
|
|
KEYWORD
| nonn,tabl,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 02 2005
|
|
|
EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu) and Christian G. Bower (bowerc(AT)usa.net), Jun 05 2005
|
| |
|
|
