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 + 5 * A( 3*x/5 + 2*A(x)/5 )^2.
(2) A(x) = -3*x/2 + 5/2 * Series_Reversion(x - 2*A(x)^2).
(3) R(x) = -2*x/3 + 5/3 * Series_Reversion(x + 3*A(x)^2), where R(A(x)) = x.
(4) R( sqrt( x/5 - R(x)/5 ) ) = 2*x/5 + 3*R(x)/5, where R(A(x)) = x.
a(n) = Sum_{k=0..n-1} A277295(n,k) * 2^k * 5^(n-k-1).
EXAMPLE
G.f.: A(x) = x + 5*x^2 + 70*x^3 + 1425*x^4 + 35410*x^5 + 999210*x^6 + 30855820*x^7 + 1020407105*x^8 + 35642665050*x^9 + 1302725802510*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 - 2*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