A277303 G.f. satisfies: A(x - 4*A(x)^2) = x + A(x)^2.

1, 5, 90, 2425, 80630, 3065810, 128271540, 5774538945, 275743894750, 13832116773110, 723891526915820, 39323723086794730, 2208811824884144540, 127904686371063157700, 7617441454740093233000, 465691699545009287055825, 29179499379365501297165550, 1871486497257264286902367950, 122731222232573572625823907900, 8222122259910817121846641763950, 562251437460415648354364719018900

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( x/5 + 4*A(x)/5 )^2.

(2) A(x) = -x/4 + 5/4 * Series_Reversion(x - 4*A(x)^2).

(3) R(x) = -4*x + 5 * Series_Reversion(x + A(x)^2), where R(A(x)) = x.

(4) R( sqrt( x/5 - R(x)/5 ) ) = 4*x/5 + R(x)/5, where R(A(x)) = x.

a(n) = Sum_{k=0..n-1} A277295(n,k) * 4^k * 5^(n-k-1).

Example

G.f.: A(x) = x + 5*x^2 + 90*x^3 + 2425*x^4 + 80630*x^5 + 3065810*x^6 + 128271540*x^7 + 5774538945*x^8 + 275743894750*x^9 + 13832116773110*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 - 4*F^2) - 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, A277304, A277305, A277306, A277307, A277308, A277309.

Cf. A276364.

Sequence in context: A301359 A352590 A037297 * A361551 A323570 A295766

Adjacent sequences: A277300 A277301 A277302 * A277304 A277305 A277306

Keyword

nonn

Author

Paul D. Hanna, Oct 09 2016

Status

approved