Original entry on oeis.org
0, 1, 2, 7, 28, 131, 690, 4033, 25864, 180265, 1354458, 10898823, 93407828, 848739867, 8143768538, 82229315137, 871067808272, 9654457636241, 111688595475634, 1345725966256071, 16854833617813388, 219050429104638707, 2949276326665620482, 41076923039499915393
Offset: 1
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lista(m) = {P = x; M = subst(P, x, 1); print1(polcoeff(M, 0, q), ", "); Q = 2*x; M = subst(Q, x, 1); print1(polcoeff(M, 0, q), ", "); for (n=3, m, newP = n*q*Q+ 2*q*(1-q)*deriv(Q,q)+2*x*(1-q)*deriv(Q,x)+n*x*P; M = subst(newP, x, 1); print1(polcoeff(M, 0, q), ", "); P = Q; Q = newP;);} \\ Michel Marcus, Feb 12 2013
A217205
Triangle read by rows, related to Bell numbers A000110: A216963 interlaced with A217202.
Original entry on oeis.org
1, 1, 1, 1, 2, 1, 4, 7, 5, 2, 11, 28, 28, 16, 5, 41, 131, 153, 118, 71, 16, 162, 690, 872, 892, 759, 272, 61, 715, 4033, 5191, 7060, 7262, 3468, 1665, 272, 3425, 25864, 32398, 58608, 66510, 41088, 29778, 7936, 1385, 17722, 180265, 211937, 510812, 601080, 479772, 443231, 156176, 60991, 7936
Offset: 1
Triangle begins:
1
1,1
1,2,1
4,7,5,2
11,28,28,16,5
41,131,153,118,71,16
162,690,872,892,759,272,61
...
First column appears to be
A032265.
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P[1] := x y; P[n_] := P[n] = ((n-1) q + x y) P[n-1] + 2 q (1-q) D[P[n-1], q] + x (1-q) D[P[n-1], x] + (1-y) D[P[n-1], y] // Simplify;
V[1] = x y; V[n_] := V[n] = ((n-1) q + x y) V[n-1] + 2 q (1-q) D[V[n-1], q] + 2 x (1-q) D[V[n-1], x] + (1 - 2 y + q y) D[V[n-1], y] // Simplify;
Dn[n_] := P[n] /. {x -> 1, y -> 0};
Dbar[n_] := V[n] /. {x -> 1, y -> 0};
Inq[1] = 1; Inq[n_] := (Dn[n] /. q -> q^2) + q (Dbar[n] /. q -> q^2);
Table[CoefficientList[Inq[n], q], {n, 1, 10}] // Flatten (* Jean-François Alcover, Sep 25 2018 *)
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tabl(m) = { J = 1; for (d=0, poldegree(J, q), print1(polcoeff(J, d, q), ", "); ); print(""); Pa = x; Pb = x; Pa1 = subst(Pa, x, 1); Pb1 = subst(Pb, x, 1); J = subst(Pa1, q, q^2) + q*subst(Pb1, q, q^2); for (d=0, poldegree(J, q), print1(polcoeff(J, d, q), ", "); ); print(""); Qa = (1+q)*x; Qb = 2*x; for (n=3, m, Qa1 = subst(Qa, x, 1); Qb1 = subst(Qb, x, 1); J = subst(Qa1, q, q^2) + q*subst(Qb1, q, q^2); for (d=0, poldegree(J, q), print1(polcoeff(J, d, q), ", "); ); print(""); newPa = n*q*Qa + 2*q*(1-q)*deriv(Qa,q) + x*(1-q)*deriv(Qa,x) + n*x*Pa; newPb = n*q*Qb + 2*q*(1-q)*deriv(Qb,q) + 2*x*(1-q)*deriv(Qb,x) + n*x*Pb; Pa = Qa; Qa = newPa; Pb = Qb; Qb = newPb;);} \\ Michel Marcus, Feb 11 2013
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