A146751 Coefficients of a new recursive polynomial: a = 11; b = 19; c = -8; r(x,n)=(a*x + b)*r(x, n - 1) + c*r(x, n - 2).

1, 1, 1, 11, 30, 11, 201, 683, 539, 121, 3731, 14948, 17666, 8228, 1331, 69281, 319589, 495770, 349690, 115797, 14641, 1286491, 6714698, 12793781, 12031756, 6036085, 1551946, 161051, 23889081, 139173951, 312977357, 366537435, 246108555

Offset: 0

Author

Roger L. Bagula, Nov 01 2008

Keywords

• nonn

Comments

Row sums are: {1, 2, 52, 1544, 45904, 1364768, 40575808, 1206356096, 35866076416, 1066331443712, 31703014700032},

Examples

			{1}, {1, 1}, {11, 30, 11}, {201, 683, 539, 121}, {3731, 14948, 17666, 8228, 1331}, {69281, 319589, 495770, 349690, 115797, 14641}, {1286491, 6714698, 12793781, 12031756, 6036085, 1551946, 161051}, {23889081, 139173951, 312977357, 366537435, 246108555, 95766781, 20131375, 1771561}, {443600611, 2853367376, 7375132996, 10310708144, 8659685650, 4514347376, 1434642308, 255104784, 19487171}, {8237298961, 57980195257, 169010749204, 274097618212, 275982948494, 180263008046, 76754973988, 20613883796, 3176408873, 214358881}, {152959875371, 1169407059446, 3789985318735, 6984487322120, 8189472336518, 6424694807300, 3429760455814, 1233927667720, 286948592975, 39013316342, \2357947691}
		

Programs

Mathematica

Clear[r, x, n, a, b, c]; r[x, 0] = 1; r[x, 1] = (1 + x); a = 11; b = 19; c = -8; r[x_, n_] := r[x, n] = (a*x + b)*r[x, n - 1] + c*r[x, n - 2]; Table[ExpandAll[r[x, n]], {n, 0, 10}]; Table[CoefficientList[ExpandAll[r[x, n]], x], {n, 0, 10}]; Flatten[%]

Formula

a = 11; b = 19; c = -8; r(x,n)=(a*x + b)*r(x, n - 1) + c*r(x, n - 2); t(n,m)=Coefficients(r(x,n))