A152284 E.g.f.: A(x) = Sum_{n>=0} x^n*faq(n,x)/n!, where faq(n,q) = q-factorial of n.

1, 1, 1, 4, 9, 56, 295, 1674, 14273, 121960, 1101231, 11444390, 138031729, 1718676948, 22808373575, 328417372906, 5142373476225, 85771047566384, 1495194316452703, 27487818332136270, 535137393073675121

Offset

0,4

Comments

(n-1) divides a(n) for n>1.

Links

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

Eric Weisstein, q-Factorial from MathWorld.

Formula

E.g.f. A(x) special values: A(-1)= 0; radius of convergence = 1.

Example

E.g.f.: A(x) = 1 + x + x^2/2! + 4*x^3/3! + 9*x^4/4! + 56*x^5/5! +...
A(x) = 1 + x + x^2*faq(2,x)/2! + x^3*faq(3,x)/3! + x^4*faq(4,x)/4! +...
A(x) = 1 + x + x^2*(1+x)/2! + x^3*(1+x)(1+x+x^2)/3! + x^4*(1+x)(1+x+x^2)(1+x+x^2+x^3)/4! +...
The q-factorial of n is faq(n,q) = Product_{k=1..n} (q^k-1)/(q-1):
faq(0,q)=1, faq(1,q)=1, faq(2,q)=(1+q), faq(3,q)=(1+q)*(1+q+q^2), faq(4,q)=(1+q)*(1+q+q^2)*(1+q+q^2+q^3), ...

Prog

(PARI) {a(n)=local(A=sum(k=0, n, x^k/k!*prod(j=1, k, (x^j-1)/(x-1)))); n!*polcoeff(A, n)}

Crossrefs

Sequence in context: A203464 A360514 A358446 * A109717 A197859 A197997

Adjacent sequences: A152281 A152282 A152283 * A152285 A152286 A152287

Keyword

nonn

Author

Paul D. Hanna, Dec 02 2008

Status

approved