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A144387 Triangle read by rows: row n gives the coefficients in the expansion of Sum_{j=0..n} A000040(j+1)*x^j*(1 - x)^(n - j).

%I A144387 #12 Jul 15 2021 04:37:11
%S A144387 2,2,1,2,-1,4,2,-3,5,3,2,-5,8,-2,8,2,-7,13,-10,10,5,2,-9,20,-23,20,-5,
%T A144387 12,2,-11,29,-43,43,-25,17,7,2,-13,40,-72,86,-68,42,-10,16,2,-15,53,
%U A144387 -112,158,-154,110,-52,26,13,2,-17,68,-165,270,-312,264,-162,78,-13,18
%N A144387 Triangle read by rows: row n gives the coefficients in the expansion of Sum_{j=0..n} A000040(j+1)*x^j*(1 - x)^(n - j).
%C A144387 Row sums yield the primes A000040.
%H A144387 G. C. Greubel, <a href="/A144387/b144387.txt">Rows n = 0..50 of the triangle, flattened</a>
%e A144387 Triangle begins
%e A144387     2;
%e A144387     2,   1;
%e A144387     2,  -1,  4;
%e A144387     2,  -3,  5,    3;
%e A144387     2,  -5,  8,   -2,   8;
%e A144387     2,  -7, 13,  -10,  10,    5;
%e A144387     2,  -9, 20,  -23,  20,   -5,  12;
%e A144387     2, -11, 29,  -43,  43,  -25,  17,    7;
%e A144387     2, -13, 40,  -72,  86,  -68,  42,  -10, 16;
%e A144387     2, -15, 53, -112, 158, -154, 110,  -52, 26,  13;
%e A144387     2, -17, 68, -165, 270, -312, 264, -162, 78, -13, 18;
%e A144387     ...
%t A144387 p[x_, n_] = Sum[Prime[k + 1]*x^k*(1 - x)^(n - k), {k, 0, n}];
%t A144387 Table[CoefficientList[p[x, n], x], {n, 0, 10}]//Flatten
%o A144387 (Sage)
%o A144387 def p(n,x): return sum( nth_prime(j+1)*x^j*(1-x)^(n-j) for j in (0..n) )
%o A144387 def T(n): return ( p(n,x) ).full_simplify().coefficients(sparse=False)
%o A144387 [T(n) for n in (0..12)] # _G. C. Greubel_, Jul 15 2021
%Y A144387 Cf. A122753, A123018, A123019, A123021, A123027, A123199, A123202, A123217, A123221, A141720, A144400, A174128.
%K A144387 sign,tabl
%O A144387 0,1
%A A144387 _Roger L. Bagula_ and _Gary W. Adamson_, Oct 01 2008
%E A144387 Edited, new name, and offset corrected by _Franck Maminirina Ramaharo_, Oct 19 2018