A274738 E.g.f. satisfies: A(x) = exp( x * Integral A(x) dx ).

1, 2, 20, 480, 21200, 1495040, 154090560, 21851648000, 4080788691200, 970763776819200, 286589492301132800, 102814798964090470400, 44054406432402362880000, 22221550008574568038400000, 13033785372897433673984000000, 8796017673121387398310133760000, 6767531687276918248610686607360000, 5888477519317946191613742861516800000, 5753199370152454677482310592627507200000, 6271818135933778813784553455691078041600000

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

Cf. A274739.

Sequence in context: A210901 A274572 A292396 * A352250 A012816 A012340

Adjacent sequences: A274735 A274736 A274737 * A274739 A274740 A274741

Keyword

nonn

Author

Paul D. Hanna, Jul 05 2016

Status

approved