%I #40 Sep 16 2019 08:23:36

%S 1,1,2,1,5,6,1,10,31,30,1,17,101,247,210,1,28,288,1358,2927,2310,1,41,

%T 652,5102,20581,40361,30030,1,58,1349,16186,107315,390238,716167,

%U 510510,1,77,2451,41817,414849,2429223,8130689,14117683,9699690

%N Triangle read by rows: T(n, k) = coefficient of x^(n-k) in Product_{m=1..n} (x+prime(m)); 0 <= k <= n, n >= 0.

%C Up to signs and order of coefficients the same as A070918. Except for signs and the first column the same as A238146. - _M. F. Hasler_, Aug 13 2015

%H Alois P. Heinz, <a href="/A260613/b260613.txt">Rows n = 0..140, flattened</a> (first 20 rows from Matthew Campbell)

%F T(n, 1) = A007504(n) for n >= 1.

%F T(n, 2) = A024447(n) for n >= 2.

%e The triangle starts:

%e Row 0: 1;

%e Row 1: 1, 2; Coefficients of x + 2.

%e Row 2: 1, 5, 6; Coefficients of (x+2)(x+3) = x^2 + 5x + 6.

%e Row 3: 1, 10, 31, 30; Coeff's of (x+2)(x+3)(x+5) = x^3 + 10x^2 + 31x + 30.

%e Row 5: 1, 17, 101, 247, 210;

%e Row 6: 1, 28, 288, 1358, 2927, 2310;

%e ...

%p T:= n-> (p-> seq(coeff(p, x, n-i), i=0..n))(mul(x+ithprime(i), i=1..n)):

%p seq(T(n), n=0..10); # _Alois P. Heinz_, Aug 18 2019

%t row[n_] := CoefficientList[Product[x + Prime[m], {m, 1, n}] + O[x]^(n+1), x] // Reverse;

%t row /@ Range[0, 8] // Flatten (* _Jean-François Alcover_, Sep 16 2019 *)

%o (PARI) tabl(nn) = {for (n=0, nn, polp = prod(k=1, n, x+prime(k)); forstep (k= n, 0, -1, print1(polcoeff(polp, k), ", ");); print(););} \\ _Michel Marcus_, Aug 10 2015

%Y Cf. A000040.

%K nonn,tabl

%O 0,3

%A _Matthew Campbell_, Aug 10 2015

%E Corrected and edited by _M. F. Hasler_, Aug 13 2015

%E a(20) in b-file corrected by _Andrew Howroyd_, Dec 31 2017