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

1, 2, 11, 184, 10121, 1911956, 1277642344, 3076635199744, 27117951046505365, 883613507047099010632, 107474419453579127300333278, 49091717449041719016035290742176, 84772868574056134938044881265953518335, 555628412000611011592987340845035908323617024, 13889914561952086638362253697842716117160344082246744

Offset

0,2

Links

Table of n, a(n) for n=0..14.

Formula

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

Example

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)); ...

Mathematica

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 *)

Prog

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

Crossrefs

Cf. A124834, A124835.

Sequence in context: A288564 A368561 A295646 * A365361 A013104 A007984

Adjacent sequences: A124833 A124834 A124835 * A124837 A124838 A124839

Keyword

nonn

Author

Paul D. Hanna, Nov 09 2006

Status

approved