A103918 - OEIS

%I #12 Dec 25 2017 03:45:55

%S 1,55,4214,463490,70548511,14302100449,3737959987644,1226167891984980,

%T 493798190899900941,239688442525550848731,138076392637292961502674,

%U 93162656724001697704101750,72792816042947595318479356875

%N Column k=4 sequence (without zero entries) of table A060524.

%C 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). - _Wolfdieter Lang_, Aug 07 2007

%F E.g.f. (with alternating zeros): A(x) = (d^4/dx^4)a(x) with a(x):=(1/(sqrt(1-x^2))*(log(sqrt((1+x)/(1-x))))^4)/4!.

%e 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).

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Feb 24 2005