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-1]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-f485cd65a8f8089f","steps":["x \u21a6 x+1"],"edges":["e-62ade03cd9f25f04"],"text":"A038335 \u2192 x \u21a6 x+1"},"headline":"A038335 \u2192 x \u21a6 x+1","chain":null}}],"oeis":[],"bfiles":[],"oeis_texts":[{"oeis_id":"","target":"node","first_row":0,"oeis_offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0:            168,             72;\n  1:           3528,           3024,             648;\n  2:          65856,          84672,           36288,            5184;\n  3:        1152480,        1975680,         1270080,          362880,           38880;\n  4:       19361664,       41489280,        35562240,        15240960,         3265920,         279936;\n  5:      316240512,      813189888,       871274880,       497871360,       160030080,       27433728,        1959552;\n  6:     5059848192,    15179544576,     19516557312,     13940398080,      5974456320,     1536288768,      219469824,      13436928;\n  7:    79692609024,   273231802368,    409847703552,    351298031616,    188195374080,    64524128256,    13826598912,    1693052928,     90699264;\n  8:  1239662807040,  4781556541440,   8196954071040,   8196954071040,   5269470474240,  2258344488960,   645241282560,  118513704960,  12697896960,   604661760;\n  9: 19090807228416, 81817745264640, 157791365867520, 180332989562880, 135249742172160, 69557010259968, 24841789378560, 6083703521280, 977738065920, 93117911040, 3990767616;\n","recurrence_sentence":"The row polynomials satisfy (n+1)*P(n,x) = (14*n+28+(6*n+12)*x)*P(n-1,x) for n >= 1, with P(0,x) = 168 + 72*x.","mathematica":"P[0, x_] := 168 + 72*x;\nP[n_, x_] := P[n, x] = Expand[Together[((14*n + 28 + (6*n + 12)*x)*P[n - 1, x])/(n + 1)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 168 + 72*x; for(n = 1, N, my(i = n + 1); v[i] = ((14*n + 28 + (6*n + 12)*x)*v[i - 1])/(n + 1)); 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-c11cb6bca0e3e7dc","steps":["basis A007318","D"],"edges":["e-37fb8ca4839f71ce","e-05310e1f064273fd"],"text":"A038284 \u2192 basis A007318 \u2192 D"},"headline":"A038284 \u2192 basis A007318 \u2192 D","chain":null}