OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..440
FORMULA
a(n) = Sum_{k=0..n} C(n,k)*n!*A001045(k)/k!.
a(n) = (n!/3)*( LaguerreL(n,-2) - LaguerreL(n,1) ).
Conjecture: a(n) +(-4*n+3)*a(n-1) +(6*n^2-16*n+9)*a(n-2) -(4*n-7)*(n-2)^2*a(n-3) +(n-2)^2*(n-3)^2*a(n-4)=0. - R. J. Mathar, Feb 23 2015
a(n) ~ n^(n + 1/4) / (3*2^(3/4) * exp(n-2*sqrt(2*n)+1)) * (1 + 67/(48*sqrt(2*n))). - Vaclav Kotesovec, Nov 13 2017
MAPLE
A129695 := proc(n)
add(binomial(n, k)*n!*A001045(k)/k!, k=0..n) ;
end proc: # R. J. Mathar, Feb 23 2015
MATHEMATICA
Table[n!*(LaguerreL[n, -2] - LaguerreL[n, 1])/3, {n, 0, 20}] (* Vaclav Kotesovec, Nov 13 2017 *)
a[n_] := Sum[n!*Binomial[n, k]*((2^k -(-1)^k)/3)/k!, {k, 0, n}]; Table[a[n], {n, 0, 40}] (* G. C. Greubel, May 14 2018 *)
PROG
(PARI) for(n=0, 30, print1(sum(k=0, n, n!*binomial(n, k)*((2^k -(-1)^k)/3)/k!), ", ")) \\ G. C. Greubel, May 14 2018
(Magma) [(&+[Factorial(n)*Binomial(n, k)*((2^k -(-1)^k)/3)/Factorial(k) : k in [0..n]]): n in [0..30]]; // G. C. Greubel, May 14 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 01 2007
EXTENSIONS
Terms a(17) onward added by G. C. Greubel, May 14 2018
STATUS
approved