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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.

A383137 a(n) = Sum_{k=0..n} k^3 * 2^(n-k) * binomial(n,k).

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%I A383137 #10 Apr 17 2025 12:27:54
%S A383137 0,1,12,87,504,2565,11988,52731,221616,898857,3542940,13640319,
%T A383137 51490728,191141613,699376356,2527001955,9030245472,31955015889,
%U A383137 112093661484,390132432423,1348223301720,4629287423061,15802106905332,53651151578187,181257000301584
%N A383137 a(n) = Sum_{k=0..n} k^3 * 2^(n-k) * binomial(n,k).
%F A383137 a(n) = 3^(n-3) * n * (2 + 6*n + n^2).
%o A383137 (PARI) a(n) = 3^(n-3)*n*(2+6*n+n^2);
%Y A383137 Cf. A027471, A383136, A383138, A383139.
%K A383137 nonn,easy
%O A383137 0,3
%A A383137 _Seiichi Manyama_, Apr 17 2025