A277301 G.f. satisfies: A(x - 2*A(x)^2) = x + 3*A(x)^2.

1, 5, 70, 1425, 35410, 999210, 30855820, 1020407105, 35642665050, 1302725802510, 49490450201460, 1944619121474970, 78734794663758580, 3275324221277662900, 139667810517388712600, 6093781146211490413825, 271623891311306597652650, 12353670814537544856558950, 572686428900679117724156900, 27036308383662996662940155550, 1298856469077709523772645582300

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

Cf. A277300, A277302, A277303, A277304, A277305, A277306, A277307, A277308, A277309.

Cf. A276364.

Sequence in context: A246154 A151471 A077691 * A014231 A203528 A147629

Adjacent sequences: A277298 A277299 A277300 * A277302 A277303 A277304

Keyword

nonn

Author

Paul D. Hanna, Oct 09 2016

Status

approved