A177453 Partial sums of A001863.

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

Offset

1,3

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).

Links

Table of n, a(n) for n=1..18.

Formula

a(n) = Sum_{i=1..n} A001863(i).

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000435, A001864, A001863.

Sequence in context: A294215 A294216 A058892 * A346405 A259787 A273601

Adjacent sequences: A177450 A177451 A177452 * A177454 A177455 A177456

Keyword

nonn

Author

Jonathan Vos Post, May 09 2010

Extensions

Extended by R. J. Mathar, May 28 2010

Status

approved