%I A094262
%S A094262 1,1,2,1,1,6,12,10,3,1,14,61,124,131,70,15,1,30,240,890,1830,2226,1600,
%T A094262 630,105,1,62,841,5060,16990,35216,47062,40796,22225,6930,945,1,126,
%U A094262 2772,25410,127953,401436,836976,1196532,1182195,795718,349020,90090
%N A094262 Triangle read by rows giving the coefficients of formulae generating 
               each variety of S2(n,k) (Stirling numbers of 2nd kind). The p-th 
               row (p>=1) contains T(i,p) for i=1 to 2*p-1, where T(i,p) satisfies 
               Sum_{i=1..2*p-1} T(i,p) * C(n-p,i-1).
%C A094262 The formulae S2(n+p-1,n) obtained are those of S2(n+1,n) { A000217 } 
               (Triangular Numbers), S2(n+2,n) { A001296 }, S2(n+3,n) { A001297 
               }, S2(n+4,n) { A001298 } and so on.
%H A094262 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A094262 Milton Abramowitz and Irene A. Stegun, eds., <a href="http://www.convertit.com/
               Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</
               a> (with Formulas, Graphs and Mathematical Tables), U.S. Dept. of 
               Commerce, National Bureau of Standards, Applied Math. Series 55, 
               1964, 1046 pages (9th Printing: November 1970) - Combinatorial Analysis, 
               Table 24.4, Stirling Numbers of the Second Kind (author: Francis 
               L. Miksa), p. 835.
%H A094262 A. F. Labossiere, <a href="http://members.lycos.co.uk/sobalian/index.html">
               Sobalian Coefficients</a>.
%H A094262 A. F. Labossiere, <a href="http://members.lycos.co.uk/stereotomography/
               index.html">Miscellaneous</a>.
%H A094262 Eric Weisstein's World of Mathematics, <a href="http://www.mathworld.wolfram.com/
               StirlingNumberoftheSecondKind.html">Stirling numbers of the 2nd kind</
               a>.
%e A094262 Row 5 contains 1,30,240,890,1830,2226,1600,630,105, so the formula generating 
               S2(n+4,n) numbers
%e A094262 { A001298 } will be the following : 1 +30*(n-5) +240*C(n-5,2) +890*C(n-5,
               3) +1830*C(n-5,4)
%e A094262 +2226*C(n-5,5) +1600*C(n-5,6) +630*C(n-5,7) +105*C(n-5,8). And then substituting 
               for the 9th
%e A094262 number of such a S2(n+p-1,n) gives S2(13,9) = 359502.
%Y A094262 Cf. A008277, A000217, A001296, A001297, A001298, A094216, A008275.
%Y A094262 Sequence in context: A144089 A165891 A039763 this_sequence A123554 A025270 
               A144510
%Y A094262 Adjacent sequences: A094259 A094260 A094261 this_sequence A094263 A094264 
               A094265
%K A094262 easy,nonn,tabl
%O A094262 1,3
%A A094262 Andre F. Labossiere (boronali(AT)laposte.net), Jun 01 2004