A236954 E.g.f. satisfies: A'(x) = A(x)^7 * A(-x) with A(0) = 1.

1, 1, 6, 76, 1296, 30976, 872976, 30638656, 1205016576, 55768141696, 2815440120576, 161768220568576, 9971911862317056, 684392034689560576, 49826356469468676096, 3976369161704254898176, 333879082003664326066176, 30374928089785982961811456, 2889528935298595311805464576

Offset

0,3

Comments

Conjectures: (Start)

a(n) == 1 (mod 5) for n>=0;

a(n) == 0 (mod 17) for n>=16;

a(n) == 0 (mod 19) for n>=17;

a(n) == 0 (mod 37) for n>=36.

(End)

Links

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

Formula

E.g.f.: 1/(1 - 5*Series_Reversion( Integral (1 - 25*x^2)^(1/5) dx ))^(1/5).

Example

E.g.f.: A(x) = 1 + x + 6*x^2/2! + 76*x^3/3! + 1296*x^4/4! + 30976*x^5/5! +...
Related series.
A(x)^7 = 1 + 7*x + 84*x^2/2! + 1498*x^3/3! + 34776*x^4/4! + 1006432*x^5/5! +...
Note that 1 - 1/A(x)^5 is an odd function:
1 - 1/A(x)^5 = 5*x + 50*x^3/3! + 11000*x^5/5! + 7460000*x^7/7! + 10335200000*x^9/9! +...
where Series_Reversion((1 - 1/A(x)^5)/5) = Integral (1-25*x^2)^(1/5) dx.

Prog

(PARI) {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/(1-5*serreverse(intformal((1-25*x^2 +x*O(x^n))^(1/5))))^(1/5); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A236953, A235371, A236955, A236956, A236957, A236958.

Sequence in context: A231281 A120593 A318614 * A116874 A030044 A145165

Adjacent sequences: A236951 A236952 A236953 * A236955 A236956 A236957

Keyword

nonn

Author

Paul D. Hanna, Apr 08 2014

Status

approved