cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A128595 Row sums of triangle A128592.

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%I A128595 #7 Jan 27 2024 13:47:26
%S A128595 1,2,5,26,189,1734,19305,253370,3828825,65473006,1249937325,
%T A128595 26352843470,608142583125,15247003381854,412685556908625,
%U A128595 11993673995924378,372509404162520625,12313505304343363126,431620764875678503125
%N A128595 Row sums of triangle A128592.
%C A128595 A128592(n,k) is the coefficient of q^(nk+k) in the q-analog of the odd double factorials (2n-1)!!.
%F A128595 a(n) = Sum_{k=0..n} { [q^(nk+k)] Product_{j=1..n+1} (1-q^(2j-1))/(1-q) } for n>=0.
%t A128595 a[n_] := Sum[SeriesCoefficient[Product[(1-q^(2j-1))/(1-q), {j, 1, n+1}], {q, 0, k(n+1)}], {k, 0, n}];
%t A128595 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Jan 27 2024 *)
%o A128595 (PARI) {a(n)=sum(k=0,n,polcoeff(prod(j=1,n+1,(1-q^(2*j-1))/(1-q)),(n+1)*k,q))}
%Y A128595 Cf. A128592; A128080; A001147 ((2n-1)!!); A128593 (column 1), A128594 (column 2).
%K A128595 nonn
%O A128595 0,2
%A A128595 _Paul D. Hanna_, Mar 12 2007