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 A173008 Triangle T(n,k) read by rows: coefficient [x^k] of the polynomial Product_{i=1..n} (x + q^i) in row n, column 0<=k<=n, and q = 4. 4
 1, 4, 1, 64, 20, 1, 4096, 1344, 84, 1, 1048576, 348160, 22848, 340, 1, 1073741824, 357564416, 23744512, 371008, 1364, 1, 4398046511104, 1465657589760, 97615085568, 1543393280, 5957952, 5460, 1, 72057594037927936, 24017731997138944, 1600791219535872, 25384570585088, 99158478848, 95414592, 21844, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums are 1, 5, 85, 5525, 1419925, 1455423125, 5962868543125, 97701601079103125, 6403069829921181503125, ... (partial products of A092896). Triangle T(n,k), read by rows, given by [4,12,64,240,1024,4032,16384,...] DELTA [1,0,4,0,16,0,64,0,256,0,1024,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Oct 01 2011 LINKS Robert Israel, Table of n, a(n) for n = 0..1430 FORMULA T(n,k) = 4^n*T(n-1,k) + T(n-1,k-1) with T(0,0)=1. - Philippe Deléham, Oct 01 2011 Sum_{k=0..n} T(n, k, 4) = A309327(n+1). - G. C. Greubel, Feb 20 2021 EXAMPLE Triangle begins as:               1;               4,             1;              64,            20,           1;            4096,          1344,          84,          1;         1048576,        348160,       22848,        340,       1;      1073741824,     357564416,    23744512,     371008,    1364,    1;   4398046511104, 1465657589760, 97615085568, 1543393280, 5957952, 5460, 1; MAPLE P:= 1: A:= 1: for n from 1 to 12 do   P:= expand(P*(x+4^n));   A:= A, seq(coeff(P, x, j), j=0..n) od: A; # Robert Israel, Aug 12 2015 MATHEMATICA (* First program *) p[x_, n_, q_]= If[n==0, 1, Product[x + q^i, {i, n}]]; Table[CoefficientList[p[x, n, 4], x], {n, 0, 10}]//Flatten (* modified by G. C. Greubel, Feb 20 2021 *) (* Second program *) T[n_, k_, q_]:= If[k<0 || k>n, 0, If[k==n, 1, q^n*T[n-1, k, q] +T[n-1, k-1, q] ]]; Table[T[n, k, 4], {n, 0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, Feb 20 2021 *) PROG (Sage) def T(n, k, q):     if (k<0 or k>n): return 0     elif (k==n): return 1     else: return q^n*T(n-1, k, q) + T(n-1, k-1, q) flatten([[T(n, k, 4) for k in (0..n)] for n in (0..10)]) # G. C. Greubel, Feb 20 2021 (Magma) function T(n, k, q)   if k lt 0 or k gt n then return 0;   elif k eq n then return 1;   else return q^n*T(n-1, k, q) + T(n-1, k-1, q);   end if; return T; end function; [T(n, k, 4): k in [0..n], n in [0..10]]; // G. C. Greubel, Feb 20 2021 CROSSREFS Cf. A023531 (q=0), A007318 (q=1), A108084 (q=2), A173007 (q=3), this sequence (q=4). Cf. A092896, A108084, A309327. Sequence in context: A278578 A338681 A069740 * A298828 A114917 A100864 Adjacent sequences:  A173005 A173006 A173007 * A173009 A173010 A173011 KEYWORD nonn,tabl,easy AUTHOR Roger L. Bagula, Feb 07 2010 STATUS approved

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Last modified August 15 02:47 EDT 2022. Contains 356122 sequences. (Running on oeis4.)