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 A193554 Triangle read by rows: first column: top entry is 1, then powers of 2; rest of triangle is Pascal's triangle A007318. 3
 1, 1, 1, 2, 1, 1, 4, 1, 2, 1, 8, 1, 3, 3, 1, 16, 1, 4, 6, 4, 1, 32, 1, 5, 10, 10, 5, 1, 64, 1, 6, 15, 20, 15, 6, 1, 128, 1, 7, 21, 35, 35, 21, 7, 1, 256, 1, 8, 28, 56, 70, 56, 28, 8, 1, 512, 1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 1024, 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1, 2048, 1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The original definition of A135233 made no sense. In fact A135233 is the binomial transform of the present sequence. LINKS G. C. Greubel, Rows n = 0..100 of triangle, flattened EXAMPLE Triangle begins: 1; 1, 1; 2, 1, 1; 4, 1, 2, 1; 8, 1, 3, 3, 1; 16, 1, 4, 6, 4, 1; 32, 1, 5, 10, 10, 5, 1; 64, 1, 6, 15, 20, 15, 6, 1; ... MAPLE T:= proc(n, k) option remember; if k=n then 1 elif k=0 then 2^(n-1) else binomial(n-1, k-1) fi; end: seq(seq(T(n, k), k=0..n), n=0..12); # G. C. Greubel, Nov 20 2019 MATHEMATICA T[n_, k_]:= T[n, k]= If[k==n, 1, If[k==0, 2^(n-1), Binomial[n-1, k-1]]]; Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Nov 20 2019 *) PROG (PARI) T(n, k) = if(k==n, 1, if(k==0, 2^(n-1), binomial(n-1, k-1) )); \\ G. C. Greubel, Nov 20 2019 (Magma) function T(n, k) if k eq n then return 1; elif k eq 0 then return 2^(n-1); else return Binomial(n-1, k-1); end if; return T; end function; [T(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Nov 20 2019 (Sage) @CachedFunction def T(n, k): if (k==n): return 1 elif (k==0): return 2^(n-1) else: return binomial(n-1, k-1) [[T(n, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Nov 20 2019 CROSSREFS Cf. A000079 (row sums) Cf. A007318, A135233. Sequence in context: A199856 A301906 A302150 * A131350 A131087 A105475 Adjacent sequences: A193551 A193552 A193553 * A193555 A193556 A193557 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Jul 30 2011 STATUS approved

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Last modified December 8 03:48 EST 2022. Contains 358672 sequences. (Running on oeis4.)