A249929 G.f. A(x) satisfies: 1+x = A(x)^3 + A(x)^4 - A(x)^6.

1, 1, 6, 87, 1544, 30669, 652387, 14535220, 334846575, 7911062633, 190635605270, 4667362377021, 115772752576351, 2903222873038115, 73481220638826204, 1874686187998433232, 48159602555272931592, 1244712958804985611455, 32343121686417402278602, 844434166911645229308309

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

G.f.: 1 + Series_Reversion(x - 6*x^2 - 15*x^3 - 14*x^4 - 6*x^5 - x^6).

Example

 G.f.: A(x) = 1 + x + 6*x^2 + 87*x^3 + 1544*x^4 + 30669*x^5 +...
Related expansions.
A(x)^3 = 1 + 3*x + 21*x^2 + 298*x^3 + 5280*x^4 + 104772*x^5 +...
A(x)^4 = 1 + 4*x + 30*x^2 + 424*x^3 + 7509*x^4 + 148968*x^5 +...
A(x)^6 = 1 + 6*x + 51*x^2 + 722*x^3 + 12789*x^4 + 253740*x^5 +...
where 1+x = A(x)^3 + A(x)^4 - A(x)^6.

Prog

 (PARI) /* From 1+x = A(x)^3 + A(x)^4 - A(x)^6: */
{a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, 0); A[#A]=-Vec(Ser(A)^3+Ser(A)^4-Ser(A)^6)[#A]); A[n+1]}
for(n=0, 25, print1(a(n) , ", "))
(PARI) /* From Series Reversion: */
{a(n)=local(A=1+serreverse(x - 6*x^2 - 15*x^3 - 14*x^4 - 6*x^5 - x^6 + x^2*O(x^n))); polcoeff(A, n)}
for(n=0, 25, print1(a(n) , ", "))

Crossrefs

Cf. A249926, A249927, A249928, A249930, A249931, A249932.

Sequence in context: A369624 A047786 A181271 * A289394 A113666 A365011

Adjacent sequences: A249926 A249927 A249928 * A249930 A249931 A249932

Keyword

nonn

Author

Paul D. Hanna, Nov 27 2014

Status

approved