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A177453 Partial sums of A001863. 1
0, 1, 5, 31, 267, 3027, 42599, 715191, 13942995, 309522515, 7707841015, 212783127799, 6449579387715, 212939326904131, 7606688596589431, 292321288041079671, 12025358303201356019, 527265684696785414387 (list; graph; refs; listen; history; text; internal format)
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 *)

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

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Last modified July 28 17:00 EDT 2021. Contains 346335 sequences. (Running on oeis4.)