cp's OEIS Frontend

Examples

			Illustration of initial row polynomials.
  R_0(y) = 1;
  R_1(y) = 1 + y;
  R_2(y) = 2 + 3*y + 4*y^2;
  R_3(y) = 6 + 12*y + 22*y^2 + 36*y^3;
  R_4(y) = 24 + 60*y + 140*y^2 + 300*y^3 + 576*y^4;
  R_5(y) = 120 + 360*y + 1020*y^2 + 2700*y^3 + 6576*y^4 + 14400*y^5;
  R_6(y) = 720 + 2520*y + 8400*y^2 + 26460*y^3 + 77952*y^4 + 211680*y^5 + 518400*y^6;
  R_7(y) = 5040 + 20160*y + 77280*y^2 + 282240*y^3 + 974736*y^4 + 3151680*y^5 + 9408960*y^6 + 25401600*y^7;
  ...
Generating method.
  R_0(y) = 1, by convention;
  R_1(y) = Sum_{i=1..1} (1 + i*y);
  R_2(y) = Sum_{i=1..2, j=1..2, j<>i} (1 + i*y*(1 + j*y));
  R_3(y) = Sum_{i=1..3, j=1..3, k=1..3, i,j,k distinct} (1 + i*y*(1 + j*y*(1 + k*y)));
  R_4(y) = Sum_{i=1..4, j=1..4, k=1..4, m=1..4, i,j,k,m distinct} (1 + i*y*(1 + j*y*(1 + k*y*(1 + m*y))));
  etc.
This triangle of coefficients begins:
  1;
  1, 1;
  2, 3, 4;
  6, 12, 22, 36;
  24, 60, 140, 300, 576;
  120, 360, 1020, 2700, 6576, 14400;
  720, 2520, 8400, 26460, 77952, 211680, 518400;
  5040, 20160, 77280, 282240, 974736, 3151680, 9408960, 25401600;
  40320, 181440, 786240, 3265920, 12930624, 48444480, 170098560, 552303360, 1625702400;  ...