The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A172427 Triangle T(n, k, q) = c(n,q)/( c(k,q)*c(n-k,q) ), where c(n, q) = Product_{j=1..n} f(n, q), f(n, q) = ( (1-q^n)*(1+(-1)^n) + n!*(1-(-1)^n) )/2, and q = 2, read by rows. 3
 1, 1, 1, 1, -3, 1, 1, 6, 6, 1, 1, -15, 30, -15, 1, 1, 120, 600, 600, 120, 1, 1, -63, 2520, -6300, 2520, -63, 1, 1, 5040, 105840, 2116800, 2116800, 105840, 5040, 1, 1, -255, 428400, -4498200, 35985600, -4498200, 428400, -255, 1, 1, 362880, 30844800, 25909632000, 108820454400, 108820454400, 25909632000, 30844800, 362880, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS G. C. Greubel, Rows n = 0..30 of the triangle, flattened FORMULA T(n, k, q) = c(n,q)/( c(k,q)*c(n-k,q) ), where c(n, q) = Product_{j=1..n} f(n, q), f(n, q) = ( (1-q^n)*(1+(-1)^n) + n!*(1-(-1)^n) )/2, and q = 2. EXAMPLE Triangle begins as: 1; 1, 1; 1, -3, 1; 1, 6, 6, 1; 1, -15, 30, -15, 1; 1, 120, 600, 600, 120, 1; 1, -63, 2520, -6300, 2520, -63, 1; 1, 5040, 105840, 2116800, 2116800, 105840, 5040, 1; 1, -255, 428400, -4498200, 35985600, -4498200, 428400, -255, 1; MATHEMATICA f[n_, q_]:= ((1-q^n)*(1+(-1)^n) + n!*(1-(-1)^n))/2; c[n_, q_]:= Product[f[j, q], {j, n}]; T[n_, k_, q_]:= c[n, q]/(c[k, q]*c[n-k, q]); Table[T[n, k, 2], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, May 07 2021 *) PROG (Sage) @CachedFunction def f(n, q): return ((1-q^n)*(1+(-1)^n) + factorial(n)*(1-(-1)^n))/2 def c(n, q): return product( f(j, q) for j in (1..n) ) def T(n, k, q): return c(n, q)/(c(k, q)*c(n-k, q)) flatten([[T(n, k, 2) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, May 07 2021 CROSSREFS Cf. this sequence (q=3), A172428 (q=4), A172429 (q=5). Sequence in context: A157243 A146769 A189610 * A143362 A182823 A210866 Adjacent sequences: A172424 A172425 A172426 * A172428 A172429 A172430 KEYWORD sign,tabl AUTHOR Roger L. Bagula, Feb 02 2010 EXTENSIONS Edited by G. C. Greubel, May 07 2021 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 September 7 19:14 EDT 2024. Contains 375749 sequences. (Running on oeis4.)