A212391 a(n) = A212392(n) / n.

1, 1, 3, 14, 80, 516, 3608, 26729, 206808, 1655232, 13612512, 114466491, 980575020, 8533242324, 75267759072, 671721353474, 6056517394512, 55104831724236, 505422858053560, 4669306663437888, 43418090784597696, 406109012334694211, 3818890067546807794

Offset

1,3

Links

Paul D. Hanna, Table of n, a(n) for n = 1..200

Formula

Given g.f. A(x), then G(x) = d/dx A(x^3)/3 = Sum_{n>=1} n*a(n)*x^(3*n-1) is the g.f. of A212392 and satisfies: G(x) = (x + G(G(x)))^2.

G.f. satisfies: A’(x) = ( 1 + x*A’(x)^2 * A’(x^2*A’(x)^3) )^2 where A'(x) = d/dx A(x).

Example

G.f.: A(x) = x + x^2 + 3*x^3 + 14*x^4 + 80*x^5 + 516*x^6 + 3608*x^7 + 26729*x^8 +...
Let G(x) = d/dx A(x^3)/3, then G(x) = (x + G(G(x)))^2, where
G(x) = x^2 + 2*x^5 + 9*x^8 + 56*x^11 + 400*x^14 + 3096*x^17 + 25256*x^20 +...
G(G(x)) = x^4 + 4*x^7 + 24*x^10 + 168*x^13 + 1284*x^16 + 10384*x^19 +...

Prog

(PARI) {a(n)=local(G=x^2+x^3); for(i=1, n, G=(x+subst(G, x, G+O(x^(3*n))))^2); polcoeff(G, 3*n-1)/n}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Cf. A212392.

Sequence in context: A121873 A361770 A107596 * A000264 A009053 A202474

Adjacent sequences: A212388 A212389 A212390 * A212392 A212393 A212394

Keyword

nonn

Author

Paul D. Hanna, May 12 2012

Status

approved