A168593 G.f.: exp( Sum_{n>=1} A132303(n)*x^n/n ), where A132303(n) = sum of the cubes of the trinomial coefficients in row n of triangle A027907.

1, 3, 27, 349, 5484, 96408, 1824758, 36393090, 754696998, 16130052394, 353134333470, 7884110379006, 178908263232959, 4115917059924057, 95806493175049929, 2252809457441037107, 53443567449376649304

Offset

0,2

Comments

Self-convolution cube-root yields the integer sequence A251686.

Links

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

Example

G.f.: A(x) = 1 + 3*x + 27*x^2 + 349*x^3 + 5484*x^4 + 96408*x^5 +...
log(A(x)) = 3*x + 45*x^2/2 + 831*x^3/3 + 17181*x^4/4 + 375903*x^5/5 +...+ A132303(n)*x^n/n +...

Prog

(PARI) {A027907(n, k) = polcoeff((1+x+x^2)^n, k)}
{A132303(n) = sum(k=0, 2*n, A027907(n, k)^3)}
{a(n) = local(A); A = exp(sum(m=1, n+1, A132303(m)*x^m/m) +x*O(x^n)); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A168590, A168592, A132303, A027907, A251686.

Sequence in context: A067000 A354658 A307650 * A364431 A328182 A372201

Adjacent sequences: A168590 A168591 A168592 * A168594 A168595 A168596

Keyword

nonn

Author

Paul D. Hanna, Dec 01 2009

Status

approved