|
Search: id:A136649
|
|
|
| A136649 |
|
Binomial transform of A014070: a(n) = Sum_{k=0..n} C(n,k)*C(2^k,k). |
|
+0
1
|
|
| 1, 3, 11, 81, 2089, 211107, 76211147, 95054910473, 410422012327681, 6211807332775516467, 334327967114349983723899, 64835852334793138873642165105, 45812640033676518721399820389451657
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
FORMULA
|
G.f.: A(x) = (1/(1-x))*Sum_{n>=0} [log(1 + (2^n-1)*x) - log(1-x)]^n / n!.
|
|
MAPLE
|
(PARI) {a(n)=sum(k=0, n, binomial(n, k)*binomial(2^k, k))} (PARI) /* Using the g.f.: */ {a(n)=local(X=x+x*O(x^n)); polcoeff(sum(k=0, n, (log(1+(2^k-1)*X)-log(1-X))^k/k!)/(1-X), n)}
|
|
CROSSREFS
|
Cf. A014070 (C(2^n, n)), A134173.
Adjacent sequences: A136646 A136647 A136648 this_sequence A136650 A136651 A136652
Sequence in context: A046153 A099341 A129114 this_sequence A062580 A097495 A092148
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com) and Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 21 2008
|
|
|
Search completed in 0.002 seconds
|
