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191102976,         6879707136,         58047528960,         206391214080,         362797056000,          313456656384,          106662334464;\n  5:       4586471424,       192631799808,       1950396973056,        8668430991360,       20316635136000,        26330359136256,        17919272189952,         5015306502144;\n  6:     110075314176,      5283615080448,      62412703137792,      332867750068224,      975198486528000,      1685142984720384,      1720250130235392,       962938848411648,       228509902503936;\n  7:    2641807540224,    142657607172096,    1925877696823296,    11983239002456064,    42128574618009600,     90997721174900736,    123858009376948224,    103997395628457984,     49358138940850176,     10155995666841600;\n  8:   63403380965376,   3804202857922560,   57776330904698880,   410853908655636480,  1685142984720384000,   4367890616395235328,   7431480562616893440,   8319791650276638720,   5922976672902021120,   2437438960041984000,    442395171247620096;\n  9: 1521681143169024, 100430955449155584, 1694772373204500480, 13558178985636003840, 63553963995168768000, 192187187121390354432, 392382173706171973632, 549106248918258155520, 521221947215377858560, 321741942725541888000, 116792325209371705344, 18953525353286467584;\n","recurrence_sentence":"The row polynomials satisfy (4+(18*n+30)*x+(9*n^2+36*n+36)*x^2)*P(n,x) = (96+(432*n+1296)*x+(216*n^2+1944*n+3672)*x^2+(324*n^2+1944*n+2916)*x^3)*P(n-1,x) for n >= 1, with P(0,x) = 576 + 6912*x + 11664*x^2.","mathematica":"P[0, x_] := 576 + 6912*x + 11664*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((96 + (432*n + 1296)*x + (216*n^2 + 1944*n + 3672)*x^2 + (324*n^2 + 1944*n + 2916)*x^3)*P[n - 1, x])/(4 + (18*n + 30)*x + (9*n^2 + 36*n + 36)*x^2)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 576 + 6912*x + 11664*x^2; for(n = 1, N, my(i = n + 1); v[i] = ((96 + (432*n + 1296)*x + (216*n^2 + 1944*n + 3672)*x^2 + (324*n^2 + 1944*n + 2916)*x^3)*v[i - 1])/(4 + (18*n + 30)*x + (9*n^2 + 36*n + 36)*x^2)); 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-c1532953a6736702","steps":["basis A013610","(\u03b8+1)\u00b2"],"edges":["e-85e8843cd1dca083","e-665e97de823e68eb"],"text":"A038338 \u2192 basis A013610 \u2192 (\u03b8+1)\u00b2"},"headline":"A038338 \u2192 basis A013610 \u2192 (\u03b8+1)\u00b2","chain":null}