A182966 E.g.f.: A(x) = Product_{n>=1} (1 + 3*x^n/n)^n.
1, 3, 6, 72, 342, 3330, 36720, 366660, 4974480, 67178160, 1043189280, 16836906240, 303306806880, 5705780240160, 114832957599360, 2475901844095680, 55754442891987840, 1331875774475326080, 33292197644365820160
Offset: 0
Keywords
Examples
E.g.f.: A(x) = 1 + 3*x + 6*x^2/2! + 72*x^3/3! + 342*x^4/4! +... A(x) = (1+3x)*(1+3x^2/2)^2*(1+3x^3/3)^3*(1+3x^4/4)^4*(1+3x^5/5)^5*...
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..438
Programs
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Mathematica
nmax = 20; CoefficientList[Series[Product[(1 + 3*x^k/k)^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 07 2020 *) -
PARI
{a(n,k=3)=n!*polcoeff(prod(m=1,n,(1+k*x^m/m+x*O(x^n))^m),n)}