0,2

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). W. Lang, Aug 07 2007.

E.g.f. (with alternating zeros): A(x)=diff(a(x), x$3) with a(x):=(1/(sqrt(1-x^2))*(ln(sqrt((1+x)/(1-x))))^3)/3!.

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).

Sequence in context: A048536 A000173 A055351 this_sequence A089550 A007804 A108298

Adjacent sequences: A103914 A103915 A103916 this_sequence A103918 A103919 A103920

nonn,easy

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