|
Search: id:A060083
|
|
|
| A060083 |
|
Coefficients of even indexed Euler polynomials (rising powers without zeros). |
|
+0
6
|
|
| 1, -1, 1, 1, -2, 1, -3, 5, -3, 1, 17, -28, 14, -4, 1, -155, 255, -126, 30, -5, 1, 2073, -3410, 1683, -396, 55, -6, 1, -38227, 62881, -31031, 7293, -1001, 91, -7, 1, 929569, -1529080, 754572, -177320, 24310, -2184, 140, -8, 1, -28820619
(list; table; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
E(2*n,1/2)*(-4)^n = A000364(n) (signless Euler numbers without zeros).
|
|
REFERENCES
|
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 809.
|
|
LINKS
|
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].
|
|
FORMULA
|
E(2*n, x)= sum(a(n, m)*x^(2*m+1), m=0..n-1) + x^(2*n), n >= 1; E(0, x)=1.
T(n, k) = A102054(n, k+1) - A102054(n+1, k+1), where A102054 is matrix inverse. E.g.f.: A(x^2, y^2) = [cosh(xy)*(y-1) + exp(xy)/(exp(x)+1) + exp(-xy)/(exp(-x)+1)]/y. - Paul D. Hanna (pauldhanna(AT)juno.com), Dec 28 2004
|
|
PROGRAM
|
(PARI) {T(n, k)=local(X=x+x*O(x^(2*n)), Y=y+y*O(y^(2*k+1))); (2*n)!*polcoeff(polcoeff((cosh(X*Y)*(Y-1)+ exp(X*Y)/(exp(X)+1)+exp(-X*Y)/(exp(-X)+1))/Y, 2*n, x), 2*k, y)} (Hanna)
|
|
CROSSREFS
|
A060082 (falling powers).
Matrix inverse is A102054. Column 0 is A001469 (Genocchi numbers).
Cf. A102054, A001469.
Adjacent sequences: A060080 A060081 A060082 this_sequence A060084 A060085 A060086
Sequence in context: A106583 A081450 A019588 this_sequence A069931 A056943 A064429
|
|
KEYWORD
|
sign,easy,tabl
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Mar 29 2001
|
|
|
Search completed in 0.002 seconds
|
