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.
%I A219665 #27 Jul 17 2025 14:46:30
%S A219665 1,2,4,9,28,111,539,3150,21623,172349,1549897,15401145,168011253,
%T A219665 2003304294,25928878273,361788001016,5411160126368,86353882249912,
%U A219665 1464841397585336,26323224850512720,499551889319197566
%N A219665 One more than the partial sums of A219661.
%C A219665 Are there any cases after n>2, for which A219666(a(n)) = n! instead of n!+1 ? (At least for all terms a(3) - a(14) that number is n!+1.)
%C A219665 Compare to the conjecture given at A213710.
%F A219665 a(n) = A226061(n)+1 = A219652(n!).
%t A219665 Accumulate@ Table[Length@ NestWhileList[# - Total@ IntegerDigits[#, MixedRadix[Reverse@ Range[2, 120]]] &, (n + 1)! - 1, # > n! - 1 &] - 1, {n, 0, 8}] + 1 (* _Michael De Vlieger_, Jun 27 2016, Version 10.2 *)
%o A219665 (Scheme) (define (A219665 n) (+ 1 (A226061 n)))
%Y A219665 One more than A226061.
%Y A219665 Cf. A219652, A219666, A226061.
%Y A219665 Cf. also A213710 (analogous sequence for base-2).
%K A219665 nonn
%O A219665 1,2
%A A219665 _Antti Karttunen_, May 28 2013
%E A219665 Terms a(16) - a(21) computed from the new terms of A219661 by _Antti Karttunen_, Jun 27 2016