Search: id:A103917
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%I A103917
%S A103917 1,30,1519,122156,14466221,2379402090,519987386619,145897455555864,
%T A103917 51151581893323161,21923440338694533750,11281206541276562523975,
%U A103917 6864911325693596764930500,4877239291150357692189181125
%N A103917 Column k=3 sequence (without zero entries) of table A060524.
%C A103917 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.
%F A103917 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!.
%e A103917 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).
%Y A103917 Sequence in context: A048536 A000173 A055351 this_sequence A089550 A007804 
               A108298
%Y A103917 Adjacent sequences: A103914 A103915 A103916 this_sequence A103918 A103919 
               A103920
%K A103917 nonn,easy
%O A103917 0,2
%A A103917 Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), 
               Feb 24 2005

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