A277309 G.f. satisfies: A(x - 5*A(x)^2) = x - 3*A(x)^2.

1, 2, 28, 570, 14284, 410604, 13046728, 448252682, 16417945620, 634848045084, 25737059674104, 1088311917852828, 47813839403065432, 2175881570186952520, 102316326149365110320, 4961686220242926811690, 247733650768933667153660, 12718117037478356041212500, 670565414769224589112024760, 36274908884974158393988101900, 2011581759381610503724213971960

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. A277295, A213591, A275765, A276360, A276361, A276362, A276363.

Cf. A277300, A277301, A277302, A277303, A277304, A277305, A277306, A277307, A277308.

Cf. A276364.

Sequence in context: A240771 A012745 A143585 * A363305 A326282 A373315

Adjacent sequences: A277306 A277307 A277308 * A277310 A277311 A277312

Keyword

nonn

Author

Paul D. Hanna, Oct 09 2016

Status

approved