0,2

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). W. Lang, Aug 07 2007.

E.g.f. (with alternating zeros): A(x)=diff(a(x), x$4) with a(x):=(1/(sqrt(1-x^2))*(ln(sqrt((1+x)/(1-x))))^4)/4!.

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).

Sequence in context: A081993 A060077 A035323 this_sequence A056567 A119081 A119051

Adjacent sequences: A103915 A103916 A103917 this_sequence A103919 A103920 A103921

nonn,easy

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Feb 24 2005