A263547 E.g.f. satisfies: A(x) = exp( x * real( A(x)^I ) ), where I^2 = -1.

1, 1, 1, -2, -11, 36, 421, -1896, -35223, 201232, 5188201, -35856160, -1188970595, 9633456704, 391498316301, -3636762088064, -175238714193967, 1835360835895552, 102369229796454481, -1193179646751072768, -75645902492063337659, 971018266973866894336, 68985480327663686993141, -966900537026209266460672

Offset

0,4

Links

Table of n, a(n) for n=0..23.

Formula

E.g.f.: A(x) = exp( Series_Reversion( x/cos(x) ) ).

Example

E.g.f.: A(x) = 1 + x + x^2/2! - 2*x^3/3! - 11*x^4/4! + 36*x^5/5! + 421*x^6/6! - 1896*x^7/7! - 35223*x^8/8! + 201232*x^9/9! + 5188201*x^10/10! +...
where
log(A(x)) = x - 3*x^3/3! + 65*x^5/5! - 3787*x^7/7! + 427905*x^9/9! - 79549811*x^11/11! +...+ A036778(n)*x^(2*n-1)/(2*n-1)! +...
which equals Series_Reversion( x/cos(x) ).
Also,
A(x)^I = 1 + I*x - x^2 - 4*I*x^3 + 13*x^4 + 96*I*x^5 - 541*x^6 - 5888*I*x^7/7! + 47545*x^8/8! +...+ A058014(n)*I^n*x^n/n! +...
Further,
Series_Reversion(A(x)-1) = log(1+x)/cos(log(1+x)) = e.g.f. of A009424.

Prog

(PARI) {a(n) = my(A=1); for(i=1, n+1, A = exp(x*real(A^I) +x*O(x^n))); n!*polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
(PARI) {a(n) = my(A=1); for(i=1, n+1, A = exp( serreverse( x/cos(x +x*O(x^n))))); n!*polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A036778, A058014.

Sequence in context: A096977 A353979 A084098 * A152819 A297406 A178138

Adjacent sequences: A263544 A263545 A263546 * A263548 A263549 A263550

Keyword

sign

Author

Paul D. Hanna, Oct 20 2015

Status

approved