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A103917
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Column k=3 sequence (without zero entries) of table A060524.
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0
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1, 30, 1519, 122156, 14466221, 2379402090, 519987386619, 145897455555864, 51151581893323161, 21923440338694533750, 11281206541276562523975, 6864911325693596764930500, 4877239291150357692189181125
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n)= sum over all multinomials M2(2*n+3,k), k from {1..p(2*n+3)} restricted to partitions with exactly three odd and any nonnegative number of even parts. p(2*n+3)= A000041(2*n+3) (partition numbers) and for the M2-multinomial numbers in A-St order see A036039(2*n,k). W. Lang, Aug 07 2007.
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FORMULA
| E.g.f. (with alternating zeros): A(x)=diff(a(x), x$3) with a(x):=(1/(sqrt(1-x^2))*(ln(sqrt((1+x)/(1-x))))^3)/3!.
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EXAMPLE
| Multinomial representation for a(2): partitions of 2*2+3=7 with three odd parts: (1^2,5) with A-St position k=5; (1,3^2) with k=7; (1^3,4) with k=9; (1^2,2,3) with k=10 and (1^3,2^2) with k=13. The M2 numbers for these partitions are 504, 280, 210, 420, 105 adding up to 1519 = a(2).
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CROSSREFS
| Sequence in context: A048536 A000173 A055351 * A196464 A089550 A007804
Adjacent sequences: A103914 A103915 A103916 * A103918 A103919 A103920
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Feb 24 2005
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