A206179 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n,k)^3 * 3^k ).

1, 4, 25, 196, 1747, 16996, 175936, 1907224, 21423385, 247515796, 2925668236, 35239199704, 431207470105, 5347823877172, 67093724913313, 850241358959044, 10869754843088962, 140045452765874704, 1816842996684686656, 23716478425653945472, 311314468637807994391

Offset

0,2

Comments

Logarithmic derivative yields A206180.

Links

Table of n, a(n) for n=0..20.

Example

 G.f.: A(x) = 1 + 4*x + 25*x^2 + 196*x^3 + 1747*x^4 + 16996*x^5 +...
where
log(A(x)) = 4*x + 34*x^2/2 + 352*x^3/3 + 3946*x^4/4 + 46744*x^5/5 + 573616*x^6/6 +...+ A206180(n)*x^n/n +...

Prog

 (PARI) {a(n)=polcoeff(exp(sum(m=1, n, x^m/m*sum(k=0, m, binomial(m, k)^3*3^k))+x*O(x^n)), n)}
for(n=0, 41, print1(a(n), ", "))

Crossrefs

Cf. A206180, A206177.

Sequence in context: A322442 A036449 A051500 * A151342 A001246 A202827

Adjacent sequences: A206176 A206177 A206178 * A206180 A206181 A206182

Keyword

nonn

Author

Paul D. Hanna, Feb 04 2012

Status

approved