# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a163842 Showing 1-1 of 1 %I A163842 #14 May 08 2020 17:39:21 %S A163842 1,7,6,43,36,30,249,206,170,140,1395,1146,940,770,630,7653,6258,5112, %T A163842 4172,3402,2772,41381,33728,27470,22358,18186,14784,12012,221399, %U A163842 180018,146290,118820,96462,78276,63492 %N A163842 Triangle interpolating the swinging factorial (A056040) restricted to odd indices with its binomial transform. Same as interpolating the beta numbers 1/beta(n,n) (A002457) with (A163869). %C A163842 Triangle read by rows. For n >= 0, k >= 0 let %C A163842 T(n,k) = sum{i=k..n} binomial(n-k,n-i)*(2i+1)$ %C A163842 where i$ denotes the swinging factorial of i (A056040). %H A163842 G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened %H A163842 Peter Luschny, Die schwingende Fakultät und Orbitalsysteme, August 2011. %H A163842 Peter Luschny, Swinging Factorial. %e A163842 1 %e A163842 7, 6 %e A163842 43, 36, 30 %e A163842 249, 206, 170, 140 %e A163842 1395, 1146, 940, 770, 630 %e A163842 7653, 6258, 5112, 4172, 3402, 2772 %e A163842 41381, 33728, 27470, 22358, 18186, 14784, 12012 %p A163842 Computes n rows of the triangle. For the functions 'SumTria' and 'swing' see A163840. %p A163842 a := n -> SumTria(k->swing(2*k+1),n,true); %t A163842 sf[n_] := n!/Quotient[n, 2]!^2; t[n_, k_] := Sum[Binomial[n-k, n-i]*sf[2*i+1], {i, k, n}]; Table[t[n, k], {n, 0, 7}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Jun 28 2013 *) %Y A163842 Row sums are A163845. Cf. A056040, A163650, A163841, A163842, A163840, A002426, A000984. %K A163842 nonn,tabl %O A163842 0,2 %A A163842 _Peter Luschny_, Aug 06 2009 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE