A177453 Partial sums of A001863.
0, 1, 5, 31, 267, 3027, 42599, 715191, 13942995, 309522515, 7707841015, 212783127799, 6449579387715, 212939326904131, 7606688596589431, 292321288041079671, 12025358303201356019, 527265684696785414387
Offset: 1
Keywords
Examples
a(5) = 0 + 1 + 4 + 26 + 236 = 267 = 3 * 89.
Programs
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Maple
A001863 := proc(n) if n = 1 then 0; else add( (n-2)!*n^k/k!,k=0..n-2) ; end if; end proc: A177453 := proc(n) add(A001863(i),i=0..n) ; end proc: seq(A177453(n),n=1..20) ; # R. J. Mathar, May 28 2010
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Mathematica
Accumulate[Table[Sum[(n-2)! n^k/k!,{k,0,n-2}],{n,20}]] (* Harvey P. Dale, Jun 19 2016 *)
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Python
from math import comb def A177453(n): return sum(((sum(comb(i,k)*(i-k)**(i-k)*k**k for k in range(1,(i+1>>1)))<<1) + (0 if i&1 else comb(i,m:=i>>1)*m**i))//i//(i-1) for i in range(2,n+1)) # Chai Wah Wu, Apr 25-26 2023
Formula
a(n) = Sum_{i=1..n} A001863(i).
Extensions
Extended by R. J. Mathar, May 28 2010
Comments