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

0,3

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 ).

Links

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

Formula

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

Example

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! +...

Prog

(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), ", "))

Crossrefs

Cf. A159600, A258657, A258659.

Sequence in context: A209363 A012569 A078258 * A222186 A124246 A219010

Adjacent sequences: A258655 A258656 A258657 * A258659 A258660 A258661

Keyword

nonn

Author

Paul D. Hanna, Jun 06 2015

Status

approved