A236957 E.g.f. satisfies: A'(x) = A(x)^7 * A(-x)^4 with A(0) = 1.

1, 1, 3, 31, 297, 5521, 90843, 2421391, 56778897, 1965992161, 59991229683, 2551838332351, 96020199171897, 4840069070838001, 216719978024072523, 12622971840715547311, 655783794933664894497, 43320949673000323765441, 2562378473386758135272163, 189242342019412261693784671

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

E.g.f.: 1/(1 - 2*Series_Reversion( Integral (1 - 4*x^2)^2 dx ))^(1/2).

Example

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 31*x^3/3! + 297*x^4/4! + 5521*x^5/5! +...
Related series.
A(x)^7 = 1 + 7*x + 63*x^2/2! + 805*x^3/3! + 13041*x^4/4! + 261247*x^5/5! +...
Note that 1 - 1/A(x)^2 is an odd function:
1 - 1/A(x)^2 = 2*x + 32*x^3/3! + 4352*x^5/5! + 1605632*x^7/7! +...
where Series_Reversion((1 - 1/A(x)^2)/2) = Integral (1-4*x^2)^2 dx.

Prog

(PARI) {a(n)=local(A=1); for(i=0, n, A=1+intformal(A^7*subst(A^4, 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/(1-2*serreverse(intformal((1-4*x^2 +x*O(x^n))^(4/2))))^(1/2); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A236953, A236954, A236955, A236956, A235374, A236958.

Sequence in context: A221894 A198964 A212730 * A112425 A144579 A348709

Adjacent sequences: A236954 A236955 A236956 * A236958 A236959 A236960

Keyword

nonn

Author

Paul D. Hanna, Apr 09 2014

Status

approved