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 A102573 #21 Apr 16 2025 09:02:45
%S A102573 1,1,3,1,5,-2,1,10,15,-10,1,14,31,-46,16,1,21,105,35,-210,112,1,27,
%T A102573 183,97,-832,860,-272,1,36,378,1008,-1575,-2436,5292,-2448,1,44,586,
%U A102573 2144,-3719,-10876,31036,-26896,7936,1,55,990,6270,3465,-51513,27720,135300,-208560
%N A102573 Triangle of coefficients of polynomials in Sum_{k=0..n} binomial(n,k) * k^r.
%C A102573 For a table of coefficients of these polynomials without factors removed see A209849. - _Peter Bala_, Mar 16 2012
%D A102573 E. Kilic, Y. T. Ulutas and N. Omur, Formulas for weighted binomial sums using the powers of terms of binary recurrences, Miskolc Mathematical Notes, Vol. 13 (2012), No. 1, pp. 53-65. - From _N. J. A. Sloane_, Dec 16 2012
%H A102573 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BinomialSums.html">Binomial Sums</a>
%e A102573 Triangle begins:
%e A102573 1;
%e A102573 1, 3;
%e A102573 1, 5, -2;
%e A102573 1, 10, 15, -10;
%e A102573 1, 14, 31, -46, 16;
%e A102573 ...
%e A102573 E.g. Sum_{k=0..n} binomial(n,k) * k^4 = 2^(n-4) * n * (n+1) * (n^2 + 5*n - 2).
%Y A102573 Cf. A209849.
%K A102573 sign,tabl
%O A102573 2,3
%A A102573 _Eric W. Weisstein_, Jan 15 2005