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A274738 E.g.f. satisfies: A(x) = exp( x * Integral A(x) dx ). 2
1, 2, 20, 480, 21200, 1495040, 154090560, 21851648000, 4080788691200, 970763776819200, 286589492301132800, 102814798964090470400, 44054406432402362880000, 22221550008574568038400000, 13033785372897433673984000000, 8796017673121387398310133760000, 6767531687276918248610686607360000, 5888477519317946191613742861516800000, 5753199370152454677482310592627507200000, 6271818135933778813784553455691078041600000 (list; graph; refs; listen; history; text; internal format)
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 * A012816 A012340 A279839

Adjacent sequences:  A274735 A274736 A274737 * A274739 A274740 A274741

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 05 2016

STATUS

approved

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Last modified November 12 07:16 EST 2019. Contains 329052 sequences. (Running on oeis4.)