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A062814
a(n) = Sum_{i=0..n-1} i * (n - i)^(n - i).
1
0, 1, 6, 38, 326, 3739, 53808, 927420, 18578248, 423649565, 10828720882, 306545462810, 9518362652994, 321605286435431, 11745699035775884, 461063683165975712, 19357125741005727156, 865493449685182242777
OFFSET
1,3
COMMENTS
Partial sums of A001923. - Amiram Eldar, Mar 26 2022
LINKS
Andrew Cusumano, Problem 11724, The American Mathematical Monthly, Vol. 120, No. 7 (2013), p. 661; A Limit Computation, Solution to Problem 11724 by Hosam M. Mahmoud, ibid., Vol. 122, No. 7 (2015), pp. 706-707.
FORMULA
From Amiram Eldar, Mar 26 2022: (Start)
a(n) = Sum_{k=0..n-1} A001923(k).
Limit_{n->oo} a(n+2)/a(n+1) - a(n+1)/a(n) = e (Cusumano, 2013). (End)
MATHEMATICA
Table[Sum[i*(n - i)^(n - i), {i, 0, -1 + n}], {n, 1, 18}]
PROG
(PARI) a(n) = sum(i=0, n-1, i*(n-i)^(n-i)); \\ Michel Marcus, Mar 26 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Olivier Gérard, Jun 23 2001
STATUS
approved