The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A169656 Triangle, read by rows, T(n, k) = (-1)^n*(n!/k!)^2*binomial(n-1, k-1). 1
 -1, 4, 1, -36, -18, -1, 576, 432, 48, 1, -14400, -14400, -2400, -100, -1, 518400, 648000, 144000, 9000, 180, 1, -25401600, -38102400, -10584000, -882000, -26460, -294, -1, 1625702400, 2844979200, 948326400, 98784000, 3951360, 65856, 448, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row sums are: {-1, 5, -55, 1057, -31301, 1319581, -74996755, 5521809665, -510921831817, 58003632177301, ...}. LINKS G. C. Greubel, Rows n = 1..100 of triangle, flattened FORMULA T(n, k) = (-1)^n * (n!/k!)^2 * binomial(n-1, k-1). EXAMPLE Triangle begins as: -1; 4, 1; -36, -18, -1; 576, 432, 48, 1; -14400, -14400, -2400, -100, -1; 518400, 648000, 144000, 9000, 180, 1; -25401600, -38102400, -10584000, -882000, -26460, -294, -1; MAPLE seq(seq( (-1)^n*(n!/k!)^2*binomial(n-1, k-1), k=1..n), n=1..10); # G. C. Greubel, Nov 28 2019 MATHEMATICA T[n_, k_]:= (-1)^n*(n!/k!)^2*Binomial[n-1, k-1]; Table[T[n, k], {n, 10}, {k, n}]//Flatten PROG (PARI) T(n, k) = (-1)^n*(n!/k!)^2*binomial(n-1, k-1); \\ G. C. Greubel, Nov 28 2019 (Magma) F:=Factorial; [(-1)^n*(F(n)/F(k))^2*Binomial(n-1, k-1): k in [1..n], n in [1..10]]; // G. C. Greubel, Nov 28 2019 (Sage) f=factorial; [[(-1)^n*(f(n)/f(k))^2*binomial(n-1, k-1) for k in (1..n)] for n in (1..10)] # G. C. Greubel, Nov 28 2019 (GAP) F:=Factorial;; Flat(List([1..10], n-> List([1..n], k-> (-1)^n*(F(n)/F(k) )^2*Binomial(n-1, k-1) ))); # G. C. Greubel, Nov 28 2019 CROSSREFS Cf. A008297. Sequence in context: A329066 A144267 A011801 * A362589 A303987 A297900 Adjacent sequences: A169653 A169654 A169655 * A169657 A169658 A169659 KEYWORD sign,tabl AUTHOR Roger L. Bagula, Apr 05 2010 EXTENSIONS Edited by G. C. Greubel, Nov 28 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 16 07:19 EDT 2024. Contains 373423 sequences. (Running on oeis4.)