A062970 a(n) = 1 + Sum_{j=1..n} j^j.

1, 2, 6, 33, 289, 3414, 50070, 873613, 17650829, 405071318, 10405071318, 295716741929, 9211817190185, 312086923782438, 11424093749340454, 449317984130199829, 18896062057839751445, 846136323944176515622, 40192544399240714091046, 2018612200059554303215025

Offset

0,2

Comments

The usual convention in the OEIS is that 0^0 = 1. This sequence could therefore be defined as Sum_{j=0..n} j^j. See also A001923.

Links

T. D. Noe, Table of n, a(n) for n = 0..100

Formula

a(n) = a(n-1) + A000312(n) = A001923(n) + 1.

a(n) ~ n^n. - Vaclav Kotesovec, Nov 27 2017

Example

a(4) = 1 + 1^1 + 2^2 + 3^3 + 4^4 = 1 + 1 + 4 + 27 + 256 = 289.

Mathematica

Table[Sum[Sum[Binomial[n, k] StirlingS2[n, k] k!, {k, 0, n}], {n, 0, m}], {m, 0, 20}] (* Geoffrey Critzer, Mar 18 2009 *)
Join[{1}, Accumulate[Table[n^n, {n, 20}]]+1] (* Harvey P. Dale, Aug 31 2016 *)

Prog

(PARI) { a=0; for (n=0, 100, write("b062970.txt", n, " ", a+=n^n) ) } \\ Harry J. Smith, Aug 14 2009
(Python)
from itertools import count, accumulate, islice
def A062970_gen(): # generator of terms
    yield from accumulate((k**k for k in count(1)), initial=1)
A062970_list = list(islice(A062970_gen(), 20)) # Chai Wah Wu, Jun 17 2022

Crossrefs

Cf. A000312, A001923.

Sequence in context: A174432 A012874 A005161 * A259436 A278611 A088125

Adjacent sequences: A062967 A062968 A062969 * A062971 A062972 A062973

Keyword

nonn

Author

Henry Bottomley, Jul 23 2001

Status

approved