A212370 G.f.: 1 = Sum_{n>=0} a(n)*x^n * [ Sum_{k=0..n+1} binomial(n+1, k)^2*(-x)^k ]^2.

1, 2, 15, 234, 6019, 226656, 11629128, 774788698, 64757369211, 6615393335250, 809323719822671, 116638942433360112, 19535480098041792024, 3759317862736434388304, 823134193681237065635088, 203355215614514847510001434, 56269314099500094422938613707

Offset

0,2

Comments

Compare to the g.f. G(x) for A006013(n) = C(3*n+1,n)/(n+1), which satisfies:

(1) 1 = Sum_{n>=0} A006013(n)*x^n*[Sum_{k=0..n+1} C(n+1,k)^2*(-x)^k]^2,

(2) G(x) = (1 + x*G(x)^(3/2))^2 so that G(x)^(1/2) is an integer series.

Links

Table of n, a(n) for n=0..16.

Example

G.f.: A(x) = 1 + 2*x + 15*x^2 + 234*x^3 + 6019*x^4 + 226656*x^5 +...
Note that the square-root of the g.f., A(x)^(1/2), is an integer series:
A(x)^(1/2) = 1 + x + 7*x^2 + 110*x^3 + 2875*x^4 + 109683*x^5 +...+ A212371(n)*x^n +...

Prog

(PARI) {a(n)=if(n==0, 1, -polcoeff(sum(m=0, n-1, a(m)*x^m*sum(k=0, m+1, binomial(m+1, k)^2*(-x)^k)^2+x*O(x^n)), n))}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A212371, A247031.

Sequence in context: A161968 A294043 A326095 * A302358 A192561 A356587

Adjacent sequences: A212367 A212368 A212369 * A212371 A212372 A212373

Keyword

nonn

Author

Paul D. Hanna, May 10 2012

Status

approved