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 A101495 #23 Sep 08 2022 08:45:16 %S A101495 1,1,3,8,23,73,253,948,3817,16433,75295,365600,1874083,10108025, %T A101495 57194585,338615084,2092609701,13470059649,90137761867,625940219896, %U A101495 4503468629391,33520255302185,257764170849941,2045255722438180 %N A101495 Column 1 of triangle A101494. %C A101495 a(n) is the number of m-tuples of nonnegative integers in which n-m+1 is the maximum and appears exactly once. - _Mathew Englander_, Apr 11 2021 %H A101495 Muniru A Asiru, <a href="/A101495/b101495.txt">Table of n, a(n) for n = 0..590</a> %H A101495 Mathew Englander, <a href="/A089246/a089246.pdf">Comments on A101494 and A089246, and related sequences</a> %F A101495 From _Vladeta Jovovic_, Sep 07 2006: (Start) %F A101495 a(n) = Sum_{k=0..n} (k+1)*(n-k)^k. %F A101495 G.f.: Sum_{k>=0} x^k/(1-k*x)^2. (End) %t A101495 Join[{1},Table[Sum[(k+1)(n-k)^k,{k,0,n}],{n,30}]] (* _Harvey P. Dale_, Mar 04 2013 *) %o A101495 (GAP) List([0..30],n->Sum([0..n],k->(k+1)*(n-k)^k)); # _Muniru A Asiru_, Mar 05 2019 %o A101495 (PARI) a(n) = sum(k=0, n, (k+1)*(n-k)^k); \\ _Michel Marcus_, Mar 05 2019 %o A101495 (Magma) [(&+[(k+1)*(n-k)^k: k in [0..n]]): n in [0..30]]; // _G. C. Greubel_, Mar 05 2019 %o A101495 (Sage) [sum((k+1)*(n-k)^k for k in (0..n)) for n in (0..30)] # _G. C. Greubel_, Mar 05 2019 %Y A101495 Cf. A101494. %K A101495 nonn %O A101495 0,3 %A A101495 _Paul D. Hanna_, Jan 21 2005