OFFSET
1,2
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..300
FORMULA
G.f. A(x) also satisfies:
(1) A(x) = x + 2 * A( 5*A(x)/2 - 3*x/2 )^2.
(2) A(x) = 3*x/5 + 2/5 * Series_Reversion(x - 5*A(x)^2).
(3) R(x) = 5*x/3 - 2/3 * Series_Reversion(x - 3*A(x)^2), where R(A(x)) = x.
(4) R( sqrt( x/2 - R(x)/2 ) ) = 5*x/2 - 3*R(x)/2, where R(A(x)) = x.
a(n) = Sum_{k=0..n-1} A277295(n,k) * 5^k * 2^(n-k-1).
EXAMPLE
G.f.: A(x) = x + 2*x^2 + 28*x^3 + 570*x^4 + 14284*x^5 + 410604*x^6 + 13046728*x^7 + 448252682*x^8 + 16417945620*x^9 + 634848045084*x^10 +...
PROG
(PARI) {a(n) = my(A=[1], F=x); for(i=1, n, A=concat(A, 0); F=x*Ser(A); A[#A] = -polcoeff(subst(F, x, x-5*F^2) + 3*F^2, #A) ); A[n]}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
Cf. A276364.
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 09 2016
STATUS
approved