|
Search: id:A134531
|
|
|
| A134531 |
|
G.f.: Sum_{n>=0} a(n)*x^n/[n!*2^(n*(n-1)/2)] = LOG( Sum_{n>=0} x^n/[n!*2^(n*(n-1)/2)] ). |
|
+0
4
|
|
| 0, 1, -1, 5, -79, 3377, -362431, 93473345, -56272471039, 77442176448257, -239804482525402111, 1650172344732021412865, -24981899010711376986398719, 825164608171793476724052668417, -59053816996641612758331731690504191, 9102696765174239045811746247171452452865
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
FORMULA
|
Equals column 0 of triangle A134530, which is the matrix log of triangle A111636, where A111636(n,k) = (2^k)^(n-k)*C(n,k).
|
|
EXAMPLE
|
Let g.f. G(x) = Sum_{n>=0} a(n)*x^n/[ n! * 2^(n*(n-1)/2) ]
then exp(G(x)) = Sum_{n>=0} x^n/[ n! * 2^(n*(n-1)/2) ];
G.f.: G(x) = x - x^2/4 + 5x^3/48 - 79x^4/1536 + 3377x^5/122880 +...
exp(G(x)) = 1 + x + x^2/4 + x^3/48 + x^4/1536 + x^5/122880 +...
|
|
PROGRAM
|
(PARI) {a(n)=n!*2^(n*(n-1)/2)*polcoeff(log(sum(k=0, n, x^k/(k!*2^(k*(k-1)/2)))+x*O(x^n)), n)}
|
|
CROSSREFS
|
Cf. related triangles: A134530, A111636; A118197 (variant); A011266.
Adjacent sequences: A134528 A134529 A134530 this_sequence A134532 A134533 A134534
Sequence in context: A106939 A142114 A141828 this_sequence A062250 A131284 A105917
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Oct 30 2007
|
|
|
Search completed in 0.002 seconds
|
