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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.)