A232688 Expansion of 1/(1-x)^(1+2*x).
1, 1, 6, 24, 160, 1100, 9168, 84336, 868544, 9806688, 120754080, 1608251040, 23036978688, 353070167424, 5764504370688, 99875064159360, 1830107743518720, 35360088597841920, 718450398365755392, 15313427783968370688, 341652563064038062080, 7962756873168407869440
Offset: 0
Keywords
Examples
E.g.f.: A(x) = 1 + x + 6*x^2/2! + 24*x^3/3! + 160*x^4/4! + 1100*x^5/5! + 9168*x^6/6! +... where A(x) = 1 + (1+2*x)*x + (1+2*x)*(2+2*x)*x^2/2! + (1+2*x)*(2+2*x)*(3+2*x)*x^3/3! + (1+2*x)*(2+2*x)*(3+2*x)*(4+2*x)*x^4/4! + (1+2*x)*(2+2*x)*(3+2*x)*(4+2*x)*(5+2*x)*x^5/5! +...
Crossrefs
Cf. A073479.
Programs
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Mathematica
CoefficientList[Series[1/(1-x)^(1+2*x), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Nov 29 2013 *) -
PARI
{a(n)=n!*polcoeff(sum(m=0, n, prod(k=1, m, k+2*x)*x^m/m!)+x*O(x^n), n)} for(n=0,30,print1(a(n),", ")) -
PARI
{a(n)=n!*polcoeff((1-x+x*O(x^n))^(-1-2*x), n)} for(n=0,30,print1(a(n),", "))
Formula
E.g.f.: Sum_{n>=0} x^n/n! * Product_{k=1..n} (k + 2*x).
a(n) ~ n! * n^2/2 * (1-4*log(n)/n). - Vaclav Kotesovec, Nov 29 2013
Comments