cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A112999 Partial sums of A036740.

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%I A112999 #29 Nov 30 2020 03:59:10
%S A112999 1,5,221,331997,24883531997,139314094387531997,
%T A112999 82606411393217618227531997,6984964247224120535022357995827531997,
%U A112999 109110688415578301444592123476429107940843827531997
%N A112999 Partial sums of A036740.
%H A112999 Seiichi Manyama, <a href="/A112999/b112999.txt">Table of n, a(n) for n = 1..30</a>
%H A112999 G. L. Honaker, Jr. and Chris Caldwell, <a href="https://primes.utm.edu/curios/page.php/331997.html">Prime Curios! 331997</a>
%F A112999 a(n) = Sum_{k=1..n} (k!)^k.
%F A112999 a(n) = Sum_{k=1..n} (A000142(k))^k.
%F A112999 a(n) = Sum_{k=1..n} A036740(k).
%F A112999 a(n) = Sum_{k=1..n} A002109(k) * A000178(k-1).
%e A112999 a(1) = (1!)^1 = 1^1 = 1.
%e A112999 a(2) = (1!)^1 + (2!)^2 = 1^1 + 2^2 = 1 + 4 = 5.
%e A112999 a(3) = (1!)^1 + (2!)^2 + (3!)^3 = 1^1 + 2^2 + 6^3 = 1 + 4 + 216 = 221.
%t A112999 Table[Sum[Product[m^k,{m,1,k}],{k,1,n}],{n,1,10}] (* _Vaclav Kotesovec_, Nov 01 2014 *)
%t A112999 Accumulate[Table[(n!)^n,{n,10}]] (* _Harvey P. Dale_, Dec 23 2019 *)
%o A112999 (PARI) a(n) = sum(k=1, n, k!^k); \\ _Michel Marcus_, Nov 30 2020
%Y A112999 Cf. A000142, A000178, A002109, A036740, A339311.
%K A112999 easy,nonn
%O A112999 1,2
%A A112999 _Jonathan Vos Post_, Jan 03 2006