A275759 E.g.f. satisfies: A(x)^A(-x) = exp(2*x) * A(-x)^A(x).

1, 1, 0, -5, 0, 196, 0, -21440, 0, 4605736, 0, -1636894280, 0, 869411900176, 0, -645115754969600, 0, 637400080589929216, 0, -808996241179323833600, 0, 1282689609051390935443456, 0, -2484567925086557616137108480, 0, 5773170916638182711440802000896, 0, -15849498359717283169328377665597440, 0, 50754498157679863282024469922251431936, 0, -187503919340846371804132353057069945159680

Offset

0,4

Links

Table of n, a(n) for n=0..31.

Formula

E.g.f.: 1 + Series_Reversion( log( sqrt( (1+x)^(1-x) / (1-x)^(1+x) ) ) ).

Example

 E.g.f.: A(x) = 1 + x - 5*x^3/3! + 196*x^5/5! - 21440*x^7/7! + 4605736*x^9/9! - 1636894280*x^11/11! + 869411900176*x^13/13! - 645115754969600*x^15/15! +...
such that A(x)^A(-x) = exp(2*x) * A(-x)^A(x).
RELATED SERIES.
A(x)^A(-x) = 1 + x - 2*x^2/2! - 8*x^3/3! + 56*x^4/4! + 336*x^5/5! - 4566*x^6/6! - 36826*x^7/7! + 771840*x^8/8! + 7854064*x^9/9! - 225103120*x^10/10! - 2770846704*x^11/11! + 101183120136*x^12/12! +...
Series_Reversion(A(x) - 1) = x + 5*x^3/6 + 9*x^5/20 + 13*x^7/42 + 17*x^9/72 + 21*x^11/110 + 25*x^13/156 + 29*x^15/210 +...+ (4*n+1)*x^(2*n+1)/(2*n*(2*n+1)) +...
which equals ( (1-x)*log(1+x) - (1+x)*log(1-x) )/2.

Prog

 (PARI) {a(n) = my(A=1, X=x + x^2*O(x^n)); A = 1 + serreverse( log( sqrt( (1+X)^(1-x) / (1-X)^(1+x) ) ) ); n!*polcoeff(A, n)}
for(n=0, 40, print1(a(n), ", "))

Crossrefs

Cf. A274377.

Sequence in context: A266324 A073911 A157302 * A222327 A286483 A264884

Adjacent sequences: A275756 A275757 A275758 * A275760 A275761 A275762

Keyword

sign

Author

Paul D. Hanna, Aug 24 2016

Status

approved