A247032 G.f.: 1 = Sum_{n>=0} a(n) * x^n * Sum_{k=0..n} C(n,k)^3 * (-x)^k.

1, 1, 8, 215, 13544, 1646568, 342128448, 111806434449, 54089613731960, 36991616761628936, 34487632073741256512, 42564197996724997147672, 67876867685905911079322176, 137043021921732373141812704320, 344286933629331983612822165758464, 1060279482920092978432461141783224583

Offset

0,3

Comments

Compare g.f. to a g.f. of the Catalan numbers (A000108):

1 = Sum_{n>=0} A000108(n)*x^n * Sum_{k=0..n+1} C(n+1,k)*(-x)^k.

Links

Table of n, a(n) for n=0..15.

Formula

G.f.: 1 = 1*(1-x) + 1*x*(1-2^3*x+x^2) + 8*x^2*(1-3^3*x+3^3*x^2-x^3) + 215*x^3*(1-4^3*x+6^3*x^2-4^3*x^3+x^4) + 13544*x^4*(1-5^3*x+10^3*x^2-10^3*x^3+5^3*x^4-x^5) +...

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)^3*(-x)^k+x*O(x^n))^1 ), n))}
for(n=0, 10, print1(a(n), ", "))

Crossrefs

Cf. A180716.

Sequence in context: A081794 A221042 A358211 * A027646 A224096 A224103

Adjacent sequences: A247029 A247030 A247031 * A247033 A247034 A247035

Keyword

nonn

Author

Paul D. Hanna, Sep 09 2014

Status

approved