A182965 E.g.f.: A(x) = Product_{n>=1} (1 + 2*x^n/n)^n.
1, 2, 4, 36, 168, 1440, 13920, 134400, 1619520, 20549760, 294631680, 4449096960, 74429752320, 1312794362880, 24870628823040, 501316411115520, 10661299747338240, 239672059847700480, 5664762159214878720
Offset: 0
Keywords
Examples
E.g.f.: A(x) = 1 + 2*x + 4*x^2/2! + 36*x^3/3! + 168*x^4/4! +... A(x) = (1+2x)*(1+2x^2/2)^2*(1+2x^3/3)^3*(1+2x^4/4)^4*(1+2x^5/5)^5*...
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..439
Programs
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Mathematica
nmax = 20; CoefficientList[Series[Product[(1 + 2*x^k/k)^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 07 2020 *) -
PARI
{a(n,k=2)=n!*polcoeff(prod(m=1,n,(1+k*x^m/m+x*O(x^n))^m),n)}