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 A122496 Triangle, read by rows, defined by f[i, k, l] = binomial(k-l, i - Min(k, l))/2^(k-l), then T(n, m) = f(n, 0, m). 1
 1, 0, -2, 0, 2, 12, 0, -2, -16, -80, 0, 2, 20, 120, 560, 0, -2, -24, -168, -896, -4032, 0, 2, 28, 224, 1344, 6720, 29568, 0, -2, -32, -288, -1920, -10560, -50688, -219648, 0, 2, 36, 360, 2640, 15840, 82368, 384384, 1647360, 0, -2, -40, -440, -3520, -22880, -128128, -640640, -2928640, -12446720 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Ulam combinatorial gene law as limited triangular array. REFERENCES S. M. Ulam, Problems in Modern Mathematics, John Wiley and Sons, New York, 1960, page 87. LINKS G. C. Greubel, Rows n = 1..100 of triangle, flattened FORMULA T(n, m) = 2^m * binomial(-m, n), for 0 <= m <= n, n >= 0. - G. C. Greubel, May 15 2019 EXAMPLE Triangle begins as:   1;   0, -2;   0,  2,  12;   0, -2, -16,  -80;   0,  2,  20,  120,  560;   0, -2, -24, -168, -896, -4032; MATHEMATICA f[i_, k_, l_]:= Binomial[k-l, i-Min[k, l]]/2^(k-l); Table[f[i, 0, l], {i, 0, 12}, {l, 0, i}] // Flatten (* modified by G. C. Greubel, May 15 2019 *) PROG (PARI) {T(n, k, m) = binomial(k-m, n - min(k, m))/2^(k-m)}; for(n=0, 12, for(m=0, n, print1(T(n, 0, m), ", "))) \\ G. C. Greubel, May 15 2019 (MAGMA) [[2^m*Binomial(-m, n): m in [0..n]]: n in [0..12]]; // G. C. Greubel, May 15 2019 (Sage) [[2^m*binomial(-m, n) for m in (0..n)] for n in (0..12)] # G. C. Greubel, May 15 2019 (GAP) Flat(List([0..12], n-> List([0..n], k-> 2^k*Binomial(-k, n) ))); # G. C. Greubel, May 15 2019 CROSSREFS Sequence in context: A211910 A250406 A107094 * A335756 A230813 A177113 Adjacent sequences:  A122493 A122494 A122495 * A122497 A122498 A122499 KEYWORD sign,tabl AUTHOR Roger L. Bagula, Sep 14 2006 EXTENSIONS Edited by N. J. A. Sloane, Oct 01 2006 Edited by G. C. Greubel, May 15 2019 STATUS approved

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Last modified January 28 17:48 EST 2022. Contains 350657 sequences. (Running on oeis4.)