A216367 G.f.: Sum_{n>=0} x^n / Product_{k=0..n} (1 - k*x)^2.
1, 1, 3, 10, 40, 184, 948, 5384, 33300, 222192, 1587512, 12071776, 97206544, 825343600, 7362067888, 68772244640, 670917511424, 6818719677952, 72038876668544, 789610228149632, 8963457852609984, 105211331721594368, 1275095788516589952, 15934546466314258688
Offset: 0
Keywords
Examples
G.f.: A(x) = 1 + x + 3*x^2 + 10*x^3 + 40*x^4 + 184*x^5 + 948*x^6 +... where A(x) = 1 + x/(1-x)^2 + x^2/((1-x)*(1-2*x))^2 + x^3/((1-x)*(1-2*x)*(1-3*x))^2 + x^4/((1-x)*(1-2*x)*(1-3*x)*(1-4*x))^2 +...
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..300
Programs
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Mathematica
With[{nn=30},CoefficientList[Series[Sum[x^n/Product[(1-k*x)^2,{k,0,n}],{n,0,nn}],{x,0,nn}],x]] (* Harvey P. Dale, Dec 15 2018 *) -
PARI
{a(n)=polcoeff(sum(m=0, n, x^m/prod(k=1, m, 1-k*x +x*O(x^n))^2), n)} for(n=0,30,print1(a(n),", "))
Comments