OFFSET
0,2
COMMENTS
Primes in this sequence include: a(2)=31, a(4)=5233. Semiprimes in this sequence include: a(1) = 2^2, a(6) = 31 * 67129, a(8) = 127 * 11676991. - Jonathan Vos Post, Mar 17 2005
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..377
FORMULA
E.g.f.: 1/(1-3x)*exp(x/(1-3x)).
E.g.f.: exp(3*x) * Sum_{n>=0} x^n/n!^2 = Sum_{n>=0} a(n)*x^n/n!^2. [Paul D. Hanna, Nov 18 2011]
a(n) = 2*(3*n-1)*a(n-1) - 9*(n-1)^2*a(n-2). - Vaclav Kotesovec, Sep 29 2013
a(n) ~ (3*n)^(n+1/4)*exp(2*sqrt(n/3)-n-1/6)/sqrt(2) * (1 + 103/(144*sqrt(3*n))). - Vaclav Kotesovec, Sep 29 2013
MAPLE
seq(sum('binomial(k, i)^2*i!*3^i', 'i'=0..k), k=0..30);
MATHEMATICA
f[n_] := Sum[k!*3^k*Binomial[n, k]^2, {k, 0, n}]; Table[ f[n], {n, 0, 16}] (* or *)
Range[0, 16]! CoefficientList[ Series[1/(1 - 3x)*Exp[x/(1 - 3x)], {x, 0, 16}], x] (* Robert G. Wilson v, Mar 16 2005 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Miklos Kristof, Mar 16 2005
EXTENSIONS
More terms from Robert G. Wilson v, Mar 16 2005
STATUS
approved