A258658 E.g.f. A(x) satisfies: A(x) = exp( Integral A(x)^3 * Integral 1/A(x)^9 dx dx ).

1, 1, 3, 123, 3129, 313929, 23062347, 4461062067, 655619300721, 207299066045841, 51139145307699603, 23947711418548452843, 8930007221716001596329, 5800583064218449362313689, 3049682921576823757255485147, 2622347479175212075411836474147, 1849810669560927151969244969258721

Offset: 0

Author

Paul D. Hanna, Jun 06 2015

Keywords

• nonn

Comments

More generally, we have the identity for real t:

* if G(x) = exp( Integral G(x)^t * Integral 1/G(x)^(3*t) dx dx ),

then G(x) = exp( Integral 1/G(x)^t * Integral G(x)^(3*t) dx dx ).

Examples

			E.g.f. A(x) = 1 + x^2/2! + 3*x^4/4! + 123*x^6/6! + 3129*x^8/8! + 313929*x^10/10! +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..180

Crossrefs

Cf. A159600, A258657, A258659.

Programs

PARI

{a(n) = local(A=1+x); for(i=1,n, A = exp( intformal( A^3 * intformal(1/A^9 + x*O(x^n)) ) ) ); n!*polcoeff(A,n)}
for(n=0,20,print1(a(2*n),", "))

PARI

{a(n) = local(A=1+x); for(i=1,n, A = exp( intformal( 1/A^3 * intformal(A^9 + x*O(x^n)) ) ) ); n!*polcoeff(A,n)}
for(n=0,20,print1(a(2*n),", "))

Formula

E.g.f. A(x) satisfies: A(x) = exp( Integral 1/A(x)^3 * Integral A(x)^9 dx dx ).