|
Search: id:A093615
|
|
|
| A093615 |
|
E.g.f. equals the ratio of two power series, each with triangular exponents of x. |
|
+0
1
|
|
| 0, 1, -1, 3, -15, 85, -570, 4509, -40804, 414864, -4686570, 58245650, -789691134, 11598605460, -183459343613, 3109122970590, -56203651969935, 1079493501290439, -21953265755518782, 471258656426134701, -10648683969964745520, 252651472831081785300
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
E.g.f. is asymptotic to 1-1/(2x). Compare to e.g.f. of A093523.
|
|
FORMULA
|
E.g.f: T1(x)/T0(x), where T0(x) = sum_{n>=0} x^(n*(n+1)/2)/(n*(n+1)/2)! and T1(x) = sum_{n>=0} x^(n*(n+1)/2+1)/(n*(n+1)/2+1)!; T0(r)=0 at r=-0.8851021553904208809237177147294641529670...
|
|
PROGRAM
|
(PARI) T0(x)=sum(k=0, sqrtint(2*n)+1, x^(k*(k+1)/2)/(k*(k+1)/2)!) (PARI) T1(x)=sum(k=0, sqrtint(2*n)+1, x^(k*(k+1)/2+1)/(k*(k+1)/2+1)!) (PARI) a(n)=n!*polcoeff(T1(x)/T0(x)+x*O(x^n), n)
|
|
CROSSREFS
|
Cf. A093523.
Sequence in context: A118342 A084209 A127085 this_sequence A001931 A075841 A152596
Adjacent sequences: A093612 A093613 A093614 this_sequence A093616 A093617 A093618
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Apr 05 2004
|
|
|
Search completed in 0.002 seconds
|
