|
Search: id:A130522
|
|
|
| A130522 |
|
Diagonal immediately below the main diagonal of triangle A130521. |
|
+0
2
|
|
| 1, 1, 3, 8, 25, 89, 349, 1496, 6962, 34861, 186678, 1063591, 6418167, 40860485, 273513831, 1919284246, 14080876273, 107750778177, 858195666410, 7100543662976, 60922480229704, 541193416875432, 4970306167860426
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
G.f. of column 0 (A127782) satisfies: G(x) = 1 + x*G(x+x^2); main diagonal of triangle A130521 equals column 0 shift left one place.
|
|
FORMULA
|
a(n) = Sum_{k=0..[n/2]+1} [C(n-k,k) + C(n-k+1,k-1)]*a(n-k-1) for n>=2, with a(0)=a(1)=1.
|
|
PROGRAM
|
(PARI) {a(n)=if(n<0, 0, if(n<=1, 1, sum(k=0, n\2+1, (binomial(n-k, k)+binomial(n-k+1, k-1))*a(n-k-1))))}
|
|
CROSSREFS
|
Cf. A130521 (triangle), A127782 (column 0).
Adjacent sequences: A130519 A130520 A130521 this_sequence A130523 A130524 A130525
Sequence in context: A045900 A000738 A033483 this_sequence A006219 A009268 A024430
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Jun 02 2007
|
|
|
Search completed in 0.002 seconds
|
