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A258662 E.g.f. A(x) satisfies: A(x) = exp( Integral A(x) * Integral 1/A(x)^2 dx dx ). 2
1, 1, 4, 40, 760, 23200, 1038400, 64081600, 5214880000, 541085248000, 69718686400000, 10921720817920000, 2044231370959360000, 450550323286412800000, 115495483535461427200000, 34070943029324134912000000, 11460293146666575236608000000, 4360020024970859812710400000000, 1862768688935303816870072320000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..150

FORMULA

E.g.f.: 1 / [ Sum_{n>=0} (-1)^n * A063902(n) * x^(2*n) / (2*n)! ].

From Vaclav Kotesovec, Jun 14 2015: (Start)

a(n) ~ c * d^n * n!^2 / sqrt(n), where d = 3*A258895 = 96*Pi / (Gamma(1/6) * Gamma(1/3))^2 = 2^(17/3) * Pi^2 / Gamma(1/3)^6 = 1.3563128975502615865238..., c = 0.8047308283353177558313... = 12/(Gamma(1/3)*Gamma(1/6)) = 2^(7/3)*sqrt(3*Pi) / Gamma(1/3)^3.

a(n) ~ 2^(5*n+3) * 3^(n+1) * Pi^(n+1) * n^(2*n+1/2) / (exp(2*n) * Gamma(1/6)^(2*n+1) * Gamma(1/3)^(2*n+1)).

a(n) ~ sqrt(3) * 2^((17*n+10)/3) * Pi^(2*n+3/2) * n^(2*n+1/2) / (exp(2*n) * Gamma(1/3)^(6*n+3)).

(End)

EXAMPLE

E.g.f.: A(x) = 1 + x^2/2! + 4*x^4/4! + 40*x^6/6! + 760*x^8/8! + 23200*x^10/10! +...

PROG

(PARI) {a(n) = local(A=1+x); for(i=1, n, A = exp( intformal( A * intformal(1/A^2 + x*O(x^n)) ) ) ); n!*polcoeff(A, n)}

for(n=0, 20, print1(a(2*n), ", "))

CROSSREFS

Cf. A063902, A258895.

Sequence in context: A251574 A010792 A064422 * A140701 A277748 A278590

Adjacent sequences:  A258659 A258660 A258661 * A258663 A258664 A258665

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 06 2015

STATUS

approved

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Last modified October 14 02:29 EDT 2019. Contains 327995 sequences. (Running on oeis4.)