A062814 a(n) = Sum_{i=0..n-1} i * (n - i)^(n - i).

0, 1, 6, 38, 326, 3739, 53808, 927420, 18578248, 423649565, 10828720882, 306545462810, 9518362652994, 321605286435431, 11745699035775884, 461063683165975712, 19357125741005727156, 865493449685182242777

Offset: 1

Author

Olivier Gérard, Jun 23 2001

Keywords

• nonn
• easy

Comments

Partial sums of A001923. - Amiram Eldar, Mar 26 2022

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..387
• 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.

Crossrefs

Cf. A001113, A001923, A062813.

Programs

Mathematica

Table[Sum[i*(n - i)^(n - i), {i, 0, -1 + n}], {n, 1, 18}]

PARI

a(n) = sum(i=0, n-1, i*(n-i)^(n-i)); \\ Michel Marcus, Mar 26 2019

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)