|
%I #12 Jul 06 2016 02:50:26
%S 1,2,20,480,21200,1495040,154090560,21851648000,4080788691200,
%T 970763776819200,286589492301132800,102814798964090470400,
%U 44054406432402362880000,22221550008574568038400000,13033785372897433673984000000,8796017673121387398310133760000,6767531687276918248610686607360000,5888477519317946191613742861516800000,5753199370152454677482310592627507200000,6271818135933778813784553455691078041600000
%N E.g.f. satisfies: A(x) = exp( x * Integral A(x) dx ).
%C Since the e.g.f. is an even function, this sequence consists of the coefficients of only the even powers of x.
%H Paul D. Hanna, <a href="/A274738/b274738.txt">Table of n, a(n) for n = 0..200</a>
%F E.g.f. A(x) equals the logarithmic derivative of the e.g.f. of A274739.
%F a(n) ~ c * n!^2 * d^n / sqrt(n), where d = 3.0991310195... and c = 0.8742487... . - _Vaclav Kotesovec_, Jul 06 2016
%e 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! +...
%e where A(x) = exp( x * Integral A(x) dx ).
%o (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)}
%o for(n=0, 20, print1(a(n), ", "))
%Y Cf. A274739.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jul 05 2016
| 