|
Search: id:A114422
|
|
|
| A114422 |
|
Riordan array (1/sqrt(1-2x-3x^2), M(x)-1) where M(x) is the g.f. of the Motzkin numbers A001006. |
|
+0
14
|
|
| 1, 1, 1, 3, 3, 1, 7, 9, 5, 1, 19, 26, 19, 7, 1, 51, 75, 65, 33, 9, 1, 141, 216, 211, 132, 51, 11, 1, 393, 623, 665, 483, 235, 73, 13, 1, 1107, 1800, 2058, 1674, 963, 382, 99, 15, 1, 3139, 5211, 6294, 5598, 3663, 1739, 581, 129, 17, 1, 8953, 15115, 19095, 18261, 13243
(list; table; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
First column is central trinomial numbers A002426. Second column is A005774. Third column is A025568. Row sums are A116387. Diagonal sums are A116388. Product of A007318 and A116382. Column k has e.g.f. exp(x)*sum{j=0..k, C(k,j)*Bessel_I(k+j,2x)}.
|
|
FORMULA
|
Riordan array (1/sqrt(1-2x-3x^2), (1-x-2x^2-sqrt(1-2x-3x^2))/(2x^2)); Number triangle T(n,k)=sum{j=0..n, C(n,j-k)C(j,n-j)}.
|
|
EXAMPLE
|
Triangle begins
1,
1, 1,
3, 3, 1,
7, 9, 5, 1,
19, 26, 19, 7, 1,
51, 75, 65, 33, 9, 1,
141, 216, 211, 132, 51, 11, 1
|
|
CROSSREFS
|
Adjacent sequences: A114419 A114420 A114421 this_sequence A114423 A114424 A114425
Sequence in context: A084144 A116401 A106479 this_sequence A127501 A118408 A079268
|
|
KEYWORD
|
easy,nonn,tabl
|
|
AUTHOR
|
Paul Barry (pbarry(AT)wit.ie), Feb 12 2006
|
|
|
Search completed in 0.002 seconds
|
