A103917 - OEIS

%I #12 Dec 25 2017 04:02:54

%S 1,30,1519,122156,14466221,2379402090,519987386619,145897455555864,

%T 51151581893323161,21923440338694533750,11281206541276562523975,

%U 6864911325693596764930500,4877239291150357692189181125

%N Column k=3 sequence (without zero entries) of table A060524.

%C 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). - _Wolfdieter Lang_, Aug 07 2007

%F E.g.f. (with alternating zeros): A(x) = (d^3/dx^3)a(x) with a(x):=(1/(sqrt(1-x^2))*(log(sqrt((1+x)/(1-x))))^3)/3!.

%e 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).

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Feb 24 2005