A206155 G.f.: exp( Sum_{n>=1} A206156(n)*x^n/n ), where A206156(n) = Sum_{k=0..n} binomial(n,k)^(2*k).

1, 2, 5, 38, 1425, 283002, 448468978, 2707673843860, 67018498701021670, 14506787732148113566364, 13603174532364904984495776225, 43960529641219941452921634596223366, 1207327102995668834632770987833295579308107, 188859837731175560954429490131760211759694331013582

Offset

0,2

Comments

Logarithmic derivative yields A206156.

Links

Table of n, a(n) for n=0..13.

Example

G.f.: A(x) = 1 + 2*x + 5*x^2 + 38*x^3 + 1425*x^4 + 283002*x^5 +...
where the logarithm of the g.f. begins:
log(A(x)) = 2*x + 6*x^2/2 + 92*x^3/3 + 5410*x^4/4 + 1400652*x^5/5 + 2687407464*x^6/6 +...+ A206156(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-0))+x*O(x^n))), n)}
for(n=0, 16, print1(a(n), ", "))

Crossrefs

Cf. A206156 (log), A184730, A206153, A206157, A206151.

Sequence in context: A347070 A290711 A228837 * A135378 A077398 A255550

Adjacent sequences: A206152 A206153 A206154 * A206156 A206157 A206158

Keyword

nonn

Author

Paul D. Hanna, Feb 04 2012

Status

approved