0,2

a(n)= sum over all M2(2*n+5,k), k from {1..p(2*n+5)} restricted to partitions with exactly five odd and possibly even parts. p(2*n+5)= A000041(2*n+5) (partition numbers), and for the M2-multinomial numbers in A-St order see A036039(2*n+5,k).

E.g.f. (with alternating zeros): A(x)=diff(a(x), x$5) with a(x):=(1/(sqrt(1-x^2))*(ln(sqrt((1+x)/(1-x))))^5)/5! = (1/(sqrt(1-x^2))*(artanh(x)^5)/5!.

a(n)= A060524(2*n+5,5),n>=0.

Multinomial representation for a(2): partitions of 2*2+5=9 with five odd parts: (1^4,5) with A-St position k=19; (1^3,3^2) with k=21; (1^5,4) with k=24; (1^4,2,3) with k=25 and (1^5,2^2) with k=28. The M2 numbers for these partitions are 3024, 3360, 756, 2520, 378, adding up to 10038 = a(2).

Sequence in context: A109627 A095372 A015261 this_sequence A116507 A083828 A119130

Adjacent sequences: A131439 A131440 A131441 this_sequence A131443 A131444 A131445

nonn,easy

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Aug 07 2007