A230740 O.g.f.: Sum_{n>=0} x^n * Product_{k=1..n} (k*(k+1)/2 + x) / (1 + k*(k+1)/2*x).
1, 1, 3, 10, 51, 370, 3691, 48525, 812089, 16832928, 422860609, 12649706416, 444120983433, 18078156682309, 844323149201499, 44838127594166770, 2686250544297734323, 180295858504407010026, 13473490672899749784979, 1114874245392058455432873
Offset: 0
Keywords
Examples
G.f.: A(x) = 1 + x + 3*x^2 + 10*x^3 + 51*x^4 + 370*x^5 + 3691*x^6 +... where A(x) = 1 + x*(1+x)/(1+x) + x^2*(1+x)*(3+x)/((1+x)*(1+3*x)) + x^3*(1+x)*(3+x)*(6+x)/((1+x)*(1+3*x)*(1+6*x)) + x^4*(1+x)*(3+x)*(6+x)*(10+x)/((1+x)*(1+3*x)*(1+6*x)*(1+10*x)) +...
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..260
Crossrefs
Cf. A230682.
Programs
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PARI
{a(n)=polcoeff(sum(m=0, n, x^m*prod(k=1, m, k*(k+1)/2+x+x*O(x^n))/prod(k=1, m, 1+k*(k+1)/2*x+x*O(x^n))), n)} for(n=0, 20, print1(a(n), ", "))
Formula
a(n) ~ 2^(n+6) * n^(2*n+7/2) / (exp(2*n) * Pi^(2*n+5/2)). - Vaclav Kotesovec, Oct 28 2014
Comments