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A048996
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Preferred multisets: triangle of numbers refining A007318 using format described in A036038.
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29
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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, 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, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| 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).
For a signed version see A111786.
Multiplying these numbers term-by-term by A036038 yields A049019.
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LINKS
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1972.
W. Lang: First 10 rows.
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FORMULA
| A048996(n) = A036040(n) * Factorial(A036043(n)) / A036038(n).
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
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EXAMPLE
| a(17) = 4 because there are four multisets using the first four digits {0,1,2,3}: 32100, 32110, 32210 and 33210
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CROSSREFS
| Cf. A000670, A007318, A036038, A019538, A115621, A000079 (row sums).
Sequence in context: A185286 A153905 A165357 * A111786 A072811 A080027
Adjacent sequences: A048993 A048994 A048995 * A048997 A048998 A048999
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KEYWORD
| nonn,tabf
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AUTHOR
| Alford Arnold (Alford1940(AT)aol.com)
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EXTENSIONS
| More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 17 2001
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