A062814 - OEIS

%I #16 Mar 26 2022 10:16:29

%S 0,1,6,38,326,3739,53808,927420,18578248,423649565,10828720882,

%T 306545462810,9518362652994,321605286435431,11745699035775884,

%U 461063683165975712,19357125741005727156,865493449685182242777

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

%C Partial sums of A001923. - _Amiram Eldar_, Mar 26 2022

%H Seiichi Manyama, <a href="/A062814/b062814.txt">Table of n, a(n) for n = 1..387</a>

%H Andrew Cusumano, <a href="https://www.jstor.org/stable/10.4169/amer.math.monthly.120.07.660">Problem 11724</a>, The American Mathematical Monthly, Vol. 120, No. 7 (2013), p. 661; <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.122.7.700">A Limit Computation</a>, Solution to Problem 11724 by Hosam M. Mahmoud, ibid., Vol. 122, No. 7 (2015), pp. 706-707.

%F From _Amiram Eldar_, Mar 26 2022: (Start)

%F a(n) = Sum_{k=0..n-1} A001923(k).

%F Limit_{n->oo} a(n+2)/a(n+1) - a(n+1)/a(n) = e (Cusumano, 2013). (End)

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

%o (PARI) a(n) = sum(i=0, n-1, i*(n-i)^(n-i)); \\ _Michel Marcus_, Mar 26 2019

%Y Cf. A001113, A001923, A062813.

%K nonn,easy

%O 1,3

%A _Olivier Gérard_, Jun 23 2001