Search: id:A048996
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%I A048996
%S A048996 1,1,1,1,2,1,1,2,1,3,1,1,2,2,3,3,4,1,1,2,2,1,3,6,1,4,6,5,1,1,2,2,2,3,6,
%T A048996 3,3,4,12,4,5,10,6,1,1,2,2,2,1,3,6,6,3,3,4,12,6,12,1,5,20,10,6,15,7,1,
%U A048996 1,2,2,2,2,3,6,6,3,3,6,1,4,12,12,12,12,4,5,20,10,30,5,6,30,20,7,21,8,1
%N A048996 Preferred multisets: triangle of numbers refining A007318 using format 
               described in A036038. Multiplying these numbers term-by-term by A036038 
               yields 1; 1,2; 1,6,6; 1,8,6,36,24; a refinement of A019538 (preferential 
               arrangements).
%C A048996 With row length A000041(n) (partition numbers) this array gives in row 
               n>=1 the multinomial numbers (call them M_0 numbers) m!/product((a_j)!,
               j=1..n) with the exponents of the partitions of n with number of 
               parts m:=sum(a_j,j=1..n), given in the Abramowitz-Stegun order. See 
               p. 831 of the given reference. See also the arrays for the M_1, M_2 
               and M_3 multinomial numbers A036038, A036039 and A036040 (or A080575).
%C A048996 For a signed version see A111786.
%H A048996 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 A048996 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/
               Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</
               a>, National Bureau of Standards Applied Math. Series 55, 1972.
%H A048996 W. Lang: <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A048996.text">
               First 10 rows.</a>
%F A048996 A048996(n) = A036040(n) * Factorial(A036043(n)) / A036038(n).
%F A048996 If the n-th partition is P, a(n) is the multinomial coefficient of the 
               signature of P. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), 
               May 30 2006
%e A048996 a(17) = 4 because there are four multisets using the first four digits 
               {0,1,2,3}: 32100, 32110, 32210 and 33210
%Y A048996 Cf. A000670, A007318, A036038, A019538.
%Y A048996 Cf. A115621.
%Y A048996 Sequence in context: A153919 A153905 A165357 this_sequence A111786 A072811 
               A080027
%Y A048996 Adjacent sequences: A048993 A048994 A048995 this_sequence A048997 A048998 
               A048999
%K A048996 nonn,tabf
%O A048996 1,5
%A A048996 Alford Arnold (Alford1940(AT)aol.com)
%E A048996 More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), 
               Jun 17 2001

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