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1: 33, 45, 9;\n 2: 1089, 4995, 4401, 1134, 81;\n 3: 35937, 438615, 945027, 653184, 177876, 19683, 729;\n 4: 1185921, 35829135, 161204985, 225501570, 130268655, 35311302, 4675806, 288684, 6561;\n 5: 39135393, 2848038975, 24997811679, 63441414540, 65591738550, 32737297041, 8618680503, 1242784620, 97332435, 3838185, 59049;\n 6: 1291467969, 223908132735, 3704470120701, 16134449124654, 27560628419121, 22584142245168, 9948364675704, 2515555424448, 377391488742, 33749160705, 1746846567, 47829690, 531441;\n 7: 42618442977, 17522950411935, 536448122592867, 3883924958644584, 10477612416964896, 13261657870542627, 8997317818048161, 3551650313738472, 858215425063518, 130618578717900, 12641272275744, 769388393340, 28280101374, 569173311, 4782969;\n 8: 1406408618241, 1368707962064895, 76743514727532945, 905841345302827290, 3752650189854881235, 7069442124710364714, 7040085434017534962, 4074442674770382948, 1458127300293687807, 336019344648290550, 51107149672713954, 5187785051593620, 350534088582930, 15456470433516, 424325877804, 6543101592, 43046721;\n 9: 46411484401953, 106822509428882655, 10907076835869797799, 207325321721816410980, 1294969695760944574650, 3543628294943886294837, 5022117492236640700731, 4098803432410374151860, 2068030654655331261645, 677173052116483979355, 148760694571658476635, 22398340486514369760, 2337886644586214976, 169432445801056662, 8443535893024338, 282131997545448, 6005404999989, 73222472421, 387420489;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (33+45*x+9*x^2)*P(n-1,x) + (45*x+18*x^2)*d/dx P(n-1,x) + 9*x^2*d^2/dx^2 P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(33 + 45*x + 9*x^2)*P[n - 1, x] + (45*x + 18*x^2)*D[P[n - 1, x], x] + 9*x^2*D[P[n - 1, x], {x, 2}]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; for(n = 1, N, my(i = n + 1); v[i] = (33 + 45*x + 9*x^2)*v[i - 1] + (45*x + 18*x^2)*deriv(v[i - 1], x) + 9*x^2*deriv(deriv(v[i - 1], x), x)); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-d3c3090977105807","steps":["basis A013610","basis A008277"],"edges":["e-0f2bf5edb3121755","e-d90757b3c8e8ec14"],"text":"A272867 \u2192 basis A013610 \u2192 basis A008277"},"headline":"A272867 \u2192 basis A013610 \u2192 basis A008277","chain":null}