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A103918
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Column k=4 sequence (without zero entries) of table A060524.
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0
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1, 55, 4214, 463490, 70548511, 14302100449, 3737959987644, 1226167891984980, 493798190899900941, 239688442525550848731, 138076392637292961502674, 93162656724001697704101750, 72792816042947595318479356875
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) = sum over all M2(2*n+4,k), k from {1..p(2*n+4)} restricted to partitions with exactly four odd and any nonnegative number of even parts. p(2*n+4)= A000041(2*n+4) (partition numbers) and for the M2-multinomial numbers in A-St order see A036039(2*n+4,k). W. Lang, Aug 07 2007.
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FORMULA
| E.g.f. (with alternating zeros): A(x)=diff(a(x), x$4) with a(x):=(1/(sqrt(1-x^2))*(ln(sqrt((1+x)/(1-x))))^4)/4!.
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EXAMPLE
| Multinomial representation for a(2): partitions of 2*2+4=8 with four odd parts: (1^3,5) with A-St position k=11; (1^2,3^2) with k=13; (1^4,4) with k=16; (1^3,2,3) with k=17 and (1^4,2^2) with k=20. The M2 numbers for these partitions are 1344, 1120, 420, 1120, 210 adding up to 4214 = a(2).
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CROSSREFS
| Sequence in context: A060077 A035323 A206097 * A013537 A056567 A119081
Adjacent sequences: A103915 A103916 A103917 * A103919 A103920 A103921
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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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