

A103918


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


0



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

0,2


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 M2multinomial numbers in ASt order see A036039(2*n+4,k).  Wolfdieter Lang, Aug 07 2007


LINKS

Table of n, a(n) for n=0..12.


FORMULA

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


EXAMPLE

Multinomial representation for a(2): partitions of 2*2+4=8 with four odd parts: (1^3,5) with ASt 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).


CROSSREFS

Sequence in context: A035323 A250833 A206097 * A013537 A056567 A119081
Adjacent sequences: A103915 A103916 A103917 * A103919 A103920 A103921


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang, Feb 24 2005


STATUS

approved



