A236958 E.g.f. satisfies: A'(x) = A(x)^7 * A(-x)^5 with A(0) = 1.

1, 1, 2, 16, 104, 1480, 16640, 337600, 5432960, 142650880, 2996614400, 96392704000, 2502799769600, 95198518604800, 2946929024000000, 129296981192704000, 4651138853703680000, 231108723265957888000, 9477883333763366912000, 525848755293052272640000, 24223777158147502407680000

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

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

Example

E.g.f.: A(x) = 1 + x + 2*x^2/2! + 16*x^3/3! + 104*x^4/4! + 1480*x^5/5! +...
Related series.
A(x)^7 = 1 + 7*x + 56*x^2/2! + 574*x^3/3! + 7280*x^4/4! + 111160*x^5/5! +...
Note that 1 - 1/A(x) is an odd function:
1 - 1/A(x) = x + 10*x^3/3! + 760*x^5/5! + 152800*x^7/7! + 58816000*x^9/9! +...
where Series_Reversion((1 - 1/A(x))) = Integral (1-x^2)^5 dx.

Prog

(PARI) {a(n)=local(A=1); for(i=0, n, A=1+intformal(A^7*subst(A^5, 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/(1-1*serreverse(intformal((1-1*x^2 +x*O(x^n))^(5/1))))^(1/1); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A236953, A236954, A236955, A236956, A236957.

Sequence in context: A370823 A059204 A187248 * A009619 A012024 A349008

Adjacent sequences: A236955 A236956 A236957 * A236959 A236960 A236961

Keyword

nonn

Author

Paul D. Hanna, Apr 09 2014

Status

approved