A208055 G.f.: exp( Sum_{n>=1} 2*Pell(n)^4 * x^n/n ), where Pell(n) = A000129(n).

1, 2, 18, 450, 11362, 311426, 8857426, 259072706, 7730804098, 234255654466, 7184570715602, 222512186923010, 6947171244623714, 218374183252085826, 6903938704875627410, 219355658720815861378, 6999679608428089841154, 224210965624588803552642

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

The o.g.f. A(x) = 1 + 2*x + 18*x^2 + 450*x^3 + ... is an algebraic function: A(x)^32 = (1 + 6*x + x^2)^4/( (1 - 34*x + x^2)*(1 - 2*x + x^2)^3 ). Cf. A207969. - Peter Bala, Apr 03 2014

Example

G.f.: A(x) = 1 + 2*x + 18*x^2 + 450*x^3 + 11362*x^4 + 311426*x^5 +...
such that, by definition,
log(A(x))/2 = x + 2^4*x^2/2 + 5^4*x^3/3 + 12^4*x^4/4 + 29^4*x^5/5 + 70^4*x^6/6 + 169^4*x^7/7 + 408^4*x^8/8 +...+ Pell(n)^4*x^n/n +...

Prog

(PARI) {Pell(n)=polcoeff(x/(1-2*x-x^2 +x*O(x^n)), n)}
{a(n)=polcoeff(exp(sum(m=1, n, 2*Pell(m)^4*x^m/m) +x*O(x^n)), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A000129, A208034, A208056, A204061, A204062, A207969.

Sequence in context: A141074 A351052 A082402 * A306655 A156907 A053916

Adjacent sequences: A208052 A208053 A208054 * A208056 A208057 A208058

Keyword

nonn

Author

Paul D. Hanna, Feb 22 2012

Status

approved