OFFSET
0,2
COMMENTS
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). - Wolfdieter Lang, Aug 07 2007
FORMULA
E.g.f. (with alternating zeros): A(x) = (d^3/dx^3)a(x) with a(x):=(1/(sqrt(1-x^2))*(log(sqrt((1+x)/(1-x))))^3)/3!.
EXAMPLE
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).
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Feb 24 2005
STATUS
approved