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Triangle by columns, (2^k, 0, 0, 0, ...).","first_index":0,"fingerprint":"f6-833b492313a93e6e","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["1"],["10","32"],["100","640","1024"]],"card_rows":[["1"],["10","32"],["100","640","1024"],["1000","9600","30720","32768"]],"row_sums_preview":["1","42","1764","74088","3111696","130691232","5489031744","230539333248"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-ae7910bbe46f8a41","steps":["basis A013611","basis A013611"],"edges":["e-d7d2422771947afc","e-3d032f99625b4202"],"text":"A130123 \u2192 basis A013611 \u2192 basis A013611"},"headline":"A130123 \u2192 basis A013611 \u2192 basis A013611","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:            160,              50;\n  1:           3840,            2400,             375;\n  2:          81920,           76800,           24000,            2500;\n  3:        1638400,         2048000,          960000,          200000,           15625;\n  4:       31457280,        49152000,        30720000,         9600000,         1500000,          93750;\n  5:      587202560,      1101004800,       860160000,       358400000,        84000000,       10500000,         546875;\n  6:    10737418240,     23488102400,     22020096000,     11468800000,      3584000000,      672000000,       70000000,       3125000;\n  7:   193273528320,    483183820800,    528482304000,    330301440000,    129024000000,    32256000000,     5040000000,     450000000,     17578125;\n  8:  3435973836800,   9663676416000,  12079595520000,   8808038400000,   4128768000000,  1290240000000,   268800000000,   36000000000,   2812500000,    97656250;\n  9: 60473139527680, 188978561024000, 265751101440000, 221459251200000, 121110528000000, 45416448000000, 11827200000000, 2112000000000, 247500000000, 17187500000, 537109375;\n","recurrence_sentence":"The row polynomials satisfy (n+1)*P(n,x) = (16*n+32+(5*n+10)*x)*P(n-1,x) for n >= 1, with P(0,x) = 160 + 50*x.","mathematica":"P[0, x_] := 160 + 50*x;\nP[n_, x_] := P[n, x] = Expand[Together[((16*n + 32 + (5*n + 10)*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] = 160 + 50*x; for(n = 1, N, my(i = n + 1); v[i] = ((16*n + 32 + (5*n + 10)*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-2bc1923905556bf6","steps":["x \u21a6 x+1","D"],"edges":["e-2406b2ec50933490","e-c4a58df08785e929"],"text":"A038319 \u2192 x \u21a6 x+1 \u2192 D"},"headline":"A038319 \u2192 x \u21a6 x+1 \u2192 D","chain":null}