A103917 Column k=3 sequence (without zero entries) of table A060524.

1, 30, 1519, 122156, 14466221, 2379402090, 519987386619, 145897455555864, 51151581893323161, 21923440338694533750, 11281206541276562523975, 6864911325693596764930500, 4877239291150357692189181125

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

Links

Table of n, a(n) for n=0..12.

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

Sequence in context: A318496 A000173 A055351 * A196464 A280360 A222719

Adjacent sequences: A103914 A103915 A103916 * A103918 A103919 A103920

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 24 2005

Status

approved