0,2

a(n)= sum over all multinomials M2(2*(n+1),k), k from {1..p(2*(n+1))} restricted to partitions with exactly two odd and any nonnegative number even parts. p(2*(n+1))= A000041(2*(n+1)) (partition numbers) and for the M2-multinomial numbers in A-St order see A036039(2*(n+1),k). W. Lang, Aug 07 2007.

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

Multinomial representation for a(2): partitions of 2*3=6 with two odd parts: (1,5) with A-St position k=2; (3^2) with k=4; (1^2,4) with k=5; (1,2,3) with k=6 and (1^2,2^2) with k=9. The M2 numbers for these partitions are 144, 40, 90, 120, 45, adding up to 439 = a(2).

Sequence in context: A041367 A041364 A033815 this_sequence A005790 A128051 A024299

Adjacent sequences: A103913 A103914 A103915 this_sequence A103917 A103918 A103919

nonn,easy

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