A103918 Column k=4 sequence (without zero entries) of table A060524.

1, 55, 4214, 463490, 70548511, 14302100449, 3737959987644, 1226167891984980, 493798190899900941, 239688442525550848731, 138076392637292961502674, 93162656724001697704101750, 72792816042947595318479356875

Offset: 0

Author

Wolfdieter Lang, Feb 24 2005

Keywords

• nonn
• easy

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). - Wolfdieter Lang, Aug 07 2007

Examples

			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).
		

Formula

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!.