A206157 G.f.: exp( Sum_{n>=1} A206158(n)*x^n/n ), where A206158(n) = Sum_{k=0..n} binomial(n,k)^(2*k+1).

1, 2, 7, 102, 6261, 2423430, 6686021554, 61335432894584, 2941073857435300366, 1190520035262419577871332, 1696475310227140760623646031573, 9980324833243234634513255755001535870, 565171444566758371735408026461987217216896790

Offset

0,2

Comments

Logarithmic derivative yields A206158.

Links

Table of n, a(n) for n=0..12.

Example

 G.f.: A(x) = 1 + 2*x + 7*x^2 + 102*x^3 + 6261*x^4 + 2423430*x^5 +...
where the logarithm of the g.f. begins:
log(A(x)) = 2*x + 10*x^2/2 + 272*x^3/3 + 24226*x^4/4 + 12053252*x^5/5 + 40086916024*x^6/6 +...+ A206158(n)*x^n/n +...

Prog

 (PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, x^m/m*sum(k=0, m, binomial(m, k)^(2*k+1))+x*O(x^n))), n)}
for(n=0, 16, print1(a(n), ", "))

Crossrefs

Cf. A206158 (log), A184730, A206153, A206155, A206151.

Sequence in context: A322642 A192342 A102598 * A102747 A122524 A229165

Adjacent sequences: A206154 A206155 A206156 * A206158 A206159 A206160

Keyword

nonn

Author

Paul D. Hanna, Feb 04 2012

Status

approved