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A129275 Column 1 of triangle A129274; a(n) is the coefficient of q^(n+2) in the squared q-factorial of n+2.

%I A129275 #12 Feb 16 2025 08:33:05
%S A129275 1,10,71,474,3103,20190,131204,853176,5555674,36237258,236763125,
%T A129275 1549496420,10156512792,66669881442,438226458380,2884072387268,
%U A129275 19002479773355,125335000366692,827479642104143,5468060901435850
%N A129275 Column 1 of triangle A129274; a(n) is the coefficient of q^(n+2) in the squared q-factorial of n+2.
%H A129275 Robert Israel, <a href="/A129275/b129275.txt">Table of n, a(n) for n = 0..300</a>
%H A129275 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/q-Factorial.html">q-Factorial</a>.
%F A129275 a(n) = [q^(n+2)] Product_{i=1..n+2} { (1-q^i)/(1-q) }^2.
%p A129275 P:= (1+q)^2: A[0]:= 1:
%p A129275 for n from 1 to 50 do
%p A129275   P:= normal(P * (1-q^(n+2))^2/(1-q)^2);
%p A129275   A[n]:= coeff(P,q,n+2);
%p A129275 od:
%p A129275 seq(A[i],i=0..50); # _Robert Israel_, Jun 25 2018
%o A129275 (PARI) a(n)=polcoeff(prod(i=1,n+2,(1-x^i)/(1-x))^2,n+2)
%Y A129275 Cf. A129274.
%K A129275 nonn
%O A129275 0,2
%A A129275 _Paul D. Hanna_, Apr 07 2007