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 A123516 Triangle read by rows: T(n,k) = (-1)^k * n! * 2^(n-2*k) * binomial(n,k) * binomial(2*k,k) (0<=k<=n). 1
 1, 2, -1, 8, -8, 3, 48, -72, 54, -15, 384, -768, 864, -480, 105, 3840, -9600, 14400, -12000, 5250, -945, 46080, -138240, 259200, -288000, 189000, -68040, 10395, 645120, -2257920, 5080320, -7056000, 6174000, -3333960, 1018710, -135135, 10321920, -41287680, 108380160, -180633600, 197568000 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums yield the double factorial numbers (A001147). REFERENCES B. T. Gill, Math. Magazine, vol. 79, No. 4, 2006, p. 313, problem 1729. LINKS G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened FORMULA T(n,0) = 2^n * n! = A000165(n). T(n,n) = (-1)^n*A001147(n). EXAMPLE Triangle begins: 1; 2,     -1; 8,     -8,      3; 48,    -72,     54,     -15; 384,   -768,    864,    -480,    105; 3840,  -9600,   14400,  -12000,  5250,   -945; 46080, -138240, 259200, -288000, 189000, -68040, 10395; ... MAPLE T:=(n, k)->(-1)^k*n!*2^(n-2*k)*binomial(n, k)*binomial(2*k, k): for n from 0 to 8 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form MATHEMATICA Table[(-1)^k*n! 2^(n - 2 k)*Binomial[n, k]*Binomial[2*k, k], {n, 0, 10}, {k, 0, n}] // Flatten (* G. C. Greubel, Oct 14 2017 *) PROG (PARI) for(n=0, 10, for(k=0, n, print1((-1)^k*n!*2^(n-2*k)*binomial(n, k)* binomial(2*k, k), ", "))) \\ G. C. Greubel, Oct 14 2017 (MAGMA) /* As triangle * / [[(-1)^k*Factorial(n)*2^(n-2*k)* Binomial(n, k)*Binomial(2*k, k): k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Oct 15 2017 CROSSREFS Cf. A001147, A000165. Sequence in context: A145901 A321369 A286724 * A193604 A016446 A254794 Adjacent sequences:  A123513 A123514 A123515 * A123517 A123518 A123519 KEYWORD sign,tabl AUTHOR Emeric Deutsch, Oct 14 2006 STATUS approved

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Last modified February 18 20:01 EST 2019. Contains 320262 sequences. (Running on oeis4.)