Original entry on oeis.org
1, 2, 4, 9, 25, 91, 444, 2920, 25996, 314752, 5201874, 117719942, 3658433597, 156505343943, 9234365056453, 752841451059559, 84938741035295776, 13279814559055121447, 2880581923860441220144, 867855593621657824023139
Offset: 0
A(x) = 1/(1-x) + x/((1-x)(1-x)) + x^2/((1-x)(1-2x)(1-x)) + x^3/((1-x)(1-3x)(1-3x)(1-x)) + x^4/((1-x)(1-4x)(1-6x)(1-4x)(1-x)) +...
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{a(n)=sum(k=0,n,polcoeff(1/prod(j=0,k,1-binomial(k,j)*x +x*O(x^n)),n-k))}
A124836
Central terms of even-indexed rows in triangle A124834.
Original entry on oeis.org
1, 2, 11, 184, 10121, 1911956, 1277642344, 3076635199744, 27117951046505365, 883613507047099010632, 107474419453579127300333278, 49091717449041719016035290742176, 84772868574056134938044881265953518335, 555628412000611011592987340845035908323617024, 13889914561952086638362253697842716117160344082246744
Offset: 0
a(0) = 1 = [x^0] 1/(1-x);
a(1) = 2 = [x^1] 1/((1-x)(1-x));
a(2) = 11 = [x^2] 1/((1-x)(1-2x)(1-x));
a(3) = 184 = [x^3] 1/((1-x)(1-3x)(1-3x)(1-x));
a(4) = 10121 = [x^4] 1/((1-x)(1-4x)(1-6x)(1-4x)(1-x));
a(5) = 1911956 = [x^5] 1/((1-x)(1-5x)(1-10x)(1-10x)(1-5x)(1-x)); ...
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a[n_] := SeriesCoefficient[Product[1/(1 - Binomial[n, k]*x) , {k, 0, n}], {x, 0, n}];
Table[a[n], {n, 0, 14}] (* Jean-François Alcover, Jul 01 2017 *)
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{a(n)=polcoeff(1/prod(j=0,n,1-binomial(n,j)*x +x*O(x^n)),n)}
Showing 1-2 of 2 results.