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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A191936 Triangle read by rows of Legendre-Stirling numbers of the first kind. 3
 1, 1, 0, 1, -2, 0, 1, -8, 12, 0, 1, -20, 108, -144, 0, 1, -40, 508, -2304, 2880, 0, 1, -70, 1708, -17544, 72000, -86400, 0, 1, -112, 4648, -89280, 808848, -3110400, 3628800, 0, 1, -168, 10920, -349568, 5808528, -48405888, 177811200, -203212800, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Apparently this is the mirror of triangle A129467. - Omar E. Pol, Jan 10 2012 LINKS G. C. Greubel, Rows n = 1..50 of the triangle, flattened G. E. Andrews, W. Gawronski and L. L. Littlejohn, The Legendre-Stirling Numbers G. E. Andrews et al., The Legendre-Stirling numbers, Discrete Math., 311 (2011), 1255-1272. J. Pan, Convolution Properties of the Generalized Stirling Numbers and the Jacobi-Stirling Numbers of the First Kind, Journal of Integer Sequences, 16 (2013), #13.9.2. FORMULA T(n, k) = ps(n-1, n-k), where ps(n, k) = ps(n-1, k-1) - n*(n-1)*ps(n-1, k), ps(n, 0) = 0, and ps(n, n) = 1. - G. C. Greubel, Jun 07 2021 EXAMPLE Triangle begins:   1;   1,    0;   1,   -2,    0;   1,   -8,   12,      0;   1,  -20,  108,   -144,      0;   1,  -40,  508,  -2304,   2880,        0;   1,  -70, 1708, -17544,  72000,   -86400,       0;   1, -112, 4648, -89280, 808848, -3110400, 3628800, 0;   ... MATHEMATICA ps[n_, k_]:= ps[n, k]= If[k==n, 1, If[k==0, 0, ps[n-1, k-1] - n*(n-1)*ps[n-1, k]]]; Table[ps[n-1, n-k], {n, 12}, {k, n}]//Flatten (* G. C. Greubel, Jun 07 2021 *) PROG (Sage) @CachedFunction def ps(n, k):     if (k==n): return 1     elif (k==0): return 0     else: return ps(n-1, k-1) - n*(n-1)*ps(n-1, k) flatten([[ps(n-1, n-k) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Jun 07 2021 CROSSREFS Cf. A191935. Sequence in context: A055141 A055140 A335330 * A327090 A021836 A255306 Adjacent sequences:  A191933 A191934 A191935 * A191937 A191938 A191939 KEYWORD sign,tabl AUTHOR N. J. A. Sloane, Jun 19 2011 EXTENSIONS More terms from Omar E. Pol, Jan 10 2012 STATUS approved

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

Last modified January 21 16:03 EST 2022. Contains 350479 sequences. (Running on oeis4.)