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 A156136 #4 Dec 05 2017 09:39:51 %S A156136 1,2,2,3,12,4,4,36,48,8,5,80,240,160,16,6,150,800,1200,480,32,7,252, %T A156136 2100,5600,5040,1344,64,8,392,4704,19600,31360,18816,3584,128,9,576, %U A156136 9408,56448,141120,150528,64512,9216,256,10,810,17280,141120,508032 %N A156136 A triangle of polynomial coefficients related to Mittag-Leffler polynomials: p(x,n)=Sum[Binomial[n, k]*Binomial[n - 1, n - k]*2^k*x^k, {k, 0, n}]/(2*x). %D A156136 Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 75-76 %F A156136 p(x,n)=Sum[Binomial[n, k]*Binomial[n - 1, n - k]*2^k*x^k, {k, 0, n}]/(2*x); %F A156136 p(x,n)=n Hypergeometric2F1[1 - n, 1 - n, 2, 2 x]; %F A156136 t(n,m)=coefficiemts(p(x,n)) %F A156136 T(n,m) = 2^m*A103371(n,m). - _R. J. Mathar_, Dec 05 2017 %e A156136 1; %e A156136 2, 2; %e A156136 3, 12, 4; %e A156136 4, 36, 48, 8; %e A156136 5, 80, 240, 160, 16; %e A156136 6, 150, 800, 1200, 480, 32; %e A156136 7, 252, 2100, 5600, 5040, 1344, 64; %e A156136 8, 392, 4704, 19600, 31360, 18816, 3584, 128; %e A156136 9, 576, 9408, 56448, 141120, 150528, 64512, 9216, 256; %e A156136 10, 810, 17280, 141120, 508032, 846720, 645120, 207360, 23040, 512; %t A156136 Clear[t0, p, x, n, m]; %t A156136 p[x_, n_] = Sum[Binomial[n, k]*Binomial[n - 1, n - k]*2^k*x^k, {k, 0, n}]/(2*x); %t A156136 Table[FullSimplify[ExpandAll[p[x, n]]], {n, 1, 10}]; %t A156136 Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 1, 10}]; %t A156136 Flatten[%] %Y A156136 A142983, A142978, A047781 (row sums). %K A156136 nonn,tabl,uned %O A156136 0,2 %A A156136 _Roger L. Bagula_, Feb 04 2009