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 A062746 #8 Apr 07 2023 17:09:43
%S A062746 1,3,-3,1,12,-29,30,-15,3,55,-222,405,-417,252,-84,12,273,-1575,4203,
%T A062746 -6678,6846,-4608,1980,-495,55,1428,-10812,38367,-83244,121518,
%U A062746 -124146,89595,-44990,15015,-3003,273,7752,-73017,325164
%N A062746 Coefficient array for certain polynomials N(3; k,x) (rising powers of x).
%C A062746 The g.f. for the sequence of column r=2*k+1, k >= 0, of array A062745(n,r) is N(3; k,x)*(x^(k+1))/(1-x)^(2*k+2) with N(3; k,x) := sum(a(k,p)*x^p,p=0..2*k).
%C A062746 The m=0 column gives: A001764(n+1). The row sums give A000012 (powers of 1) and (unsigned) A062747.
%C A062746 The sequence of step width of this staircase array is [1,2,2,2,...], i.e. the degree of the row polynomials is [0,2,4,6,...]= A005843.
%F A062746 a(k, p) := [x^p]N(3; k, x) with N(3; k, x)=(N(3; k-1, x)-A001764(k)*(1-x)^(2*k+1))/x, N(3; 0, x) := 1.
%F A062746 a(n, k)= a(n-1, k+1)+((-1)^k)*binomial(2*n+1, k+1)*binomial(3*n+1, n)/(3*n+1) if k=0, .., (2*n-3); a(n, k)= ((-1)^k)*binomial(2*n+1, k+1)*binomial(3*n+1, n)/(3*n+1) if k=(2*n-2), ..., 2*n; else 0.
%e A062746 {1}; {3,-3,1}; {12,-29,30,-15,3}; ...; N(3; 1,x)= 3-3*x+x^2.
%Y A062746 Cf. A062991.
%K A062746 sign,easy,tabf
%O A062746 0,2
%A A062746 _Wolfdieter Lang_, Jul 12 2001