cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A177453 Partial sums of A001863.

Original entry on oeis.org

0, 1, 5, 31, 267, 3027, 42599, 715191, 13942995, 309522515, 7707841015, 212783127799, 6449579387715, 212939326904131, 7606688596589431, 292321288041079671, 12025358303201356019, 527265684696785414387
Offset: 1

Views

Author

Jonathan Vos Post, May 09 2010

Keywords

Comments

Partial sums of normalized total height of rooted trees with n nodes. The subsequence of primes in the partial sums begins: 5, 31, no more through a(15).

Examples

			a(5) = 0 + 1 + 4 + 26 + 236 = 267 = 3 * 89.
		

Crossrefs

Programs

  • 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
  • Mathematica
    Accumulate[Table[Sum[(n-2)! n^k/k!,{k,0,n-2}],{n,20}]] (* Harvey P. Dale, Jun 19 2016 *)
  • 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