A131442 Sixth column (m=5) of triangle A060524 without zeros.

1, 91, 10038, 1467290, 281838271, 69542401565, 21540814788284, 8205391883388996, 3775954944255499341, 2067250635545212529775, 1328812758711335378653074, 991440081612864413673579774, 850081840027433295638565899691, 830293567537520120294141671187025

Offset: 0

Author

Wolfdieter Lang, Aug 07 2007

Keywords

• nonn
• easy

Comments

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).

Examples

			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).
		

Crossrefs

Cf. A000041, A036039, A060524.

Formula

E.g.f. (with alternating zeros): A(x) = (d^5/dx^5) a(x) with a(x):=(1/(sqrt(1-x^2))*(log(sqrt((1+x)/(1-x))))^5)/5! = (1/(sqrt(1-x^2)))*(arctanh(x)^5)/5!.

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