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

%I #2 Mar 30 2012 18:37:15

%S 1,1,1,4,9,56,295,1674,14273,121960,1101231,11444390,138031729,

%T 1718676948,22808373575,328417372906,5142373476225,85771047566384,

%U 1495194316452703,27487818332136270,535137393073675121

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

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

%H Eric Weisstein, <a href="http://mathworld.wolfram.com/q-Factorial.html">q-Factorial</a> from MathWorld.

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

%e E.g.f.: A(x) = 1 + x + x^2/2! + 4*x^3/3! + 9*x^4/4! + 56*x^5/5! +...

%e A(x) = 1 + x + x^2*faq(2,x)/2! + x^3*faq(3,x)/3! + x^4*faq(4,x)/4! +...

%e 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! +...

%e The q-factorial of n is faq(n,q) = Product_{k=1..n} (q^k-1)/(q-1):

%e 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), ...

%o (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)}

%K nonn

%O 0,4

%A _Paul D. Hanna_, Dec 02 2008

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Last modified June 4 14:20 EDT 2023. Contains 363128 sequences. (Running on oeis4.)