OFFSET
0,2
COMMENTS
Since the e.g.f. is an even function, this sequence consists of the coefficients of only the even powers of x.
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..200
FORMULA
E.g.f. A(x) equals the logarithmic derivative of the e.g.f. of A274739.
a(n) ~ c * n!^2 * d^n / sqrt(n), where d = 3.0991310195... and c = 0.8742487... . - Vaclav Kotesovec, Jul 06 2016
EXAMPLE
E.g.f.: A(x) = 1 + 2*x^2/2! + 20*x^4/4! + 480*x^6/6! + 21200*x^8/8! + 1495040*x^10/10! + 154090560*x^12/12! + 21851648000*x^14/14! + 4080788691200*x^16/16! +...
where A(x) = exp( x * Integral A(x) dx ).
PROG
(PARI) {a(n) = my(A=1); for(i=0, n, A = exp( x*intformal( A +x*O(x^(2*n)) ) ) ); (2*n)!*polcoeff(A, 2*n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 05 2016
STATUS
approved