A231173 G.f.: Sum_{n>=0} x^n * Product_{k=1..n} (k - 2*x) / (1 - 2*k*x).

1, 1, 2, 12, 98, 956, 10936, 144228, 2158408, 36163480, 670866440, 13653114768, 302484623696, 7247757117392, 186761906627200, 5150354700227136, 151354201527450784, 4721967515068611712, 155871806606752812416, 5427835405339896680640, 198851725447794931284224

Offset

0,3

Comments

Compare to a g.f. of the Pell numbers (A000129):

Sum_{n>=0} x^n * Product_{k=1..n} (2*k + x)/(1 + 2*k*x) = 1/(1-2*x-x^2).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..280

Formula

a(n) = Sum_{k=0..n} A231171(n,k)*(-2)^k for n>=0.

a(n) ~ 2^(n+1) * n! / (3 * (log(3))^(n+1)). - Vaclav Kotesovec, Nov 02 2014

Example

G.f.: A(x) = 1 + x + 2*x^2 + 12*x^3 + 98*x^4 + 956*x^5 + 10936*x^6 +...
where
A(x) = 1 + x*(1-2*x)/(1-2*x) + x^2*(1-2*x)*(2-2*x)/((1-2*x)*(1-4*x)) + x^3*(1-2*x)*(2-2*x)*(3-2*x)/((1-2*x)*(1-4*x)*(1-6*x)) + x^4*(1-2*x)*(2-2*x)*(3-2*x)*(4-2*x)/((1-2*x)*(1-4*x)*(1-6*x)*(1-8*x)) +...

Prog

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

Crossrefs

Cf. A231171, A231172.

Sequence in context: A322717 A219538 A245897 * A303203 A012548 A012550

Adjacent sequences: A231170 A231171 A231172 * A231174 A231175 A231176

Keyword

nonn

Author

Paul D. Hanna, Nov 05 2013

Status

approved