|
Search: id:A124431
|
|
|
| A124431 |
|
a(n) = Sum_{k=0..n} 2^k*C([(n+k)/2],k)*C([(n+k+1)/2],k)). |
|
+0
2
|
|
| 1, 3, 9, 29, 97, 331, 1145, 4001, 14089, 49915, 177713, 635293, 2278841, 8198227, 29567729, 106872961, 387038993, 1404052659, 5101219929, 18559193245, 67605310097, 246541193883, 899999057385, 3288522934433, 12026324883865
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
This is the inverse Motzkin transform of A026378 assuming offset 1 here. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 07 2009]
|
|
FORMULA
|
a(n) = Sum_{k=0..n} 2^k*A124428(n+k,k).
Conjecture: G.f.:-1/2*(1-4*x+x^2-((x^2+1)*(1-4*x+x^2))^(1/2))/x/(1-4*x+x^2) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009]
|
|
PROGRAM
|
(PARI) a(n)=sum(k=0, n, 2^k*binomial((n+k)\2, k)*binomial((n+k+1)\2, k))
|
|
CROSSREFS
|
Cf. A124428.
Sequence in context: A071736 A148938 A082306 this_sequence A071740 A081696 A148939
Adjacent sequences: A124428 A124429 A124430 this_sequence A124432 A124433 A124434
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Oct 31 2006
|
|
|
Search completed in 0.002 seconds
|
