OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..360
FORMULA
E.g.f. (for offset 1): log((1-x)*(1-4*x))/(4*x-5).
a(n) = n!*Sum_{k=0..n} 4^k/binomial(n, k).
a(n) = Sum_{k=0..n} k!*4^k*(n-k)!.
a(n) ~ 4^n * n! * (1 + 1/(4*n) + 1/(8*n^2) + 7/(32*n^3) + 1/(2*n^4) + 187/(128*n^5) + 1337/(256*n^6) + 22559/(1024*n^7) + 109517/(1024*n^8) + 1202047/(2048*n^9) + 14710847/(4096*n^10) + ...). - Vaclav Kotesovec, Dec 07 2020
MATHEMATICA
Table[Sum[k!*4^k*(n - k)!, {k, 0, n}], {n, 0, 50}] (* G. C. Greubel, Aug 28 2017 *)
PROG
(PARI) for(n=0, 50, print1(sum(k=0, n, k!*4^k*(n-k)!), ", ")) \\ G. C. Greubel, Aug 28 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 21 2005
STATUS
approved