A236953 E.g.f. satisfies: A'(x) = A(x)^7 / A(-x) with A(0) = 1.

1, 1, 8, 106, 2192, 57016, 1900928, 73712416, 3392081792, 174804246016, 10262192027648, 659665274853376, 47102181734254592, 3627986771528559616, 305130092337642733568, 27389239435315827367936, 2651535737853039676424192, 271778192160406582640214016, 29764289917739954089348825088

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

E.g.f.: 1/(1 - 7*Series_Reversion( Integral 1/(1 - 49*x^2)^(1/7) dx ))^(1/7).

Example

E.g.f.: A(x) = 1 + x + 8*x^2/2! + 106*x^3/3! + 2192*x^4/4! + 57016*x^5/5! +...
Related series.
A(x)^7 = 1 + 7*x + 98*x^2/2! + 1960*x^3/3! + 52136*x^4/4! + 1709512*x^5/5! +...
Note that 1 - 1/A(x)^7 is an odd function:
1 - 1/A(x)^7 = 7*x - 98*x^3/3! - 19208*x^5/5! - 14137088*x^7/7! -...
where Series_Reversion((1 - 1/A(x)^7)/7) = Integral 1/(1-49*x^2)^(1/7) dx.

Prog

(PARI) /* By definition A'(x) = A(x)^7 / A(-x): */
{a(n)=local(A=1); for(i=0, n, A=1+intformal(A^7/subst(A, x, -x) +x*O(x^n) )); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))
(PARI) {a(n)=local(A=1); A=1/(1-7*serreverse(intformal(1/(1-49*x^2 +x*O(x^n))^(1/7))))^(1/7); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A235370, A236954, A236955, A236956, A236957, A236958.

Sequence in context: A369512 A112701 A099695 * A345474 A000845 A199658

Adjacent sequences: A236950 A236951 A236952 * A236954 A236955 A236956

Keyword

nonn

Author

Paul D. Hanna, Apr 09 2014

Status

approved