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A124836 Central terms of even-indexed rows in triangle A124834. 2

%I

%S 1,2,11,184,10121,1911956,1277642344,3076635199744,27117951046505365,

%T 883613507047099010632,107474419453579127300333278,

%U 49091717449041719016035290742176,84772868574056134938044881265953518335,555628412000611011592987340845035908323617024,13889914561952086638362253697842716117160344082246744

%N Central terms of even-indexed rows in triangle A124834.

%F G.f.: A(x) = [x^n] * Product_{k=0..n} 1/(1 - binomial(n,k)*x).

%e a(0) = 1 = [x^0] 1/(1-x);

%e a(1) = 2 = [x^1] 1/((1-x)(1-x));

%e a(2) = 11 = [x^2] 1/((1-x)(1-2x)(1-x));

%e a(3) = 184 = [x^3] 1/((1-x)(1-3x)(1-3x)(1-x));

%e a(4) = 10121 = [x^4] 1/((1-x)(1-4x)(1-6x)(1-4x)(1-x));

%e a(5) = 1911956 = [x^5] 1/((1-x)(1-5x)(1-10x)(1-10x)(1-5x)(1-x)); ...

%t a[n_] := SeriesCoefficient[Product[1/(1 - Binomial[n, k]*x) , {k, 0, n}], {x, 0, n}];

%t Table[a[n], {n, 0, 14}] (* _Jean-Fran├žois Alcover_, Jul 01 2017 *)

%o (PARI) {a(n)=polcoeff(1/prod(j=0,n,1-binomial(n,j)*x +x*O(x^n)),n)}

%Y Cf. A124834, A124835.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Nov 09 2006

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Last modified August 15 15:55 EDT 2022. Contains 356148 sequences. (Running on oeis4.)