A195200 G.f. satisfies: A(x) = A(x^2)^3 + x*A(x^2)^2.

1, 1, 3, 2, 12, 7, 25, 10, 84, 37, 162, 50, 444, 140, 753, 160, 1983, 510, 3224, 570, 7890, 1591, 11886, 1572, 28770, 4889, 41844, 4680, 97524, 13356, 133621, 11440, 311973, 36616, 413907, 30490, 948118, 91823, 1195800, 69230, 2766384, 233122, 3384334, 170916, 7760430

Offset

0,3

Links

Paul D. Hanna, Table of n, a(n) for n = 0..8200

Formula

A series quadrisection of A(x) is 2*x^3*A(x^4)^5.

Series bisections of A(x)^2 are:

. (A(x)^2 + A(-x)^2)/2 = A(x^2)^6 + x^2*A(x^2)^4 and

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

Example

G.f.: A(x) = 1 + x + 3*x^2 + 2*x^3 + 12*x^4 + 7*x^5 + 25*x^6 +...
Related expansions begin:
A(x)^2 = 1 + 2*x + 7*x^2 + 10*x^3 + 37*x^4 + 50*x^5 + 140*x^6 +...
A(x)^3 = 1 + 3*x + 12*x^2 + 25*x^3 + 84*x^4 + 162*x^5 + 444*x^6 +...
A(x)^4 = 1 + 4*x + 18*x^2 + 48*x^3 + 163*x^4 + 388*x^5 + 1098*x^6 +..
A(x)^5 = 1 + 5*x + 25*x^2 + 80*x^3 + 285*x^4 + 786*x^5 + 2340*x^6 +...
A(x)^6 = 1 + 6*x + 33*x^2 + 122*x^3 + 462*x^4 + 1428*x^5 + 4501*x^6 +...
The series bisections of A(x)^2 begin:
. A(x^2)^6 + x^2*A(x^2)^4 = 1 + 7*x^2 + 37*x^4 + 140*x^6 + 510*x^8 + 1591*x^10 +...
. 2*x*A(x^2)^5 = 2*x + 10*x^3 + 50*x^5 + 160*x^7 + 570*x^9 + 1572*x^11 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, 21, A=subst(A, x, x^2+x*O(x^n))^3+x*subst(A, x, x^2+x*O(x^n))^2); polcoeff(A, n)}

Crossrefs

Cf. A174512.

Sequence in context: A122407 A346122 A232752 * A098646 A129925 A267011

Adjacent sequences: A195197 A195198 A195199 * A195201 A195202 A195203

Keyword

nonn

Author

Paul D. Hanna, Sep 12 2011

Status

approved