A111538 Column 2 of triangle A111536; also equals column 0 of triangle A111541, which is the matrix log of triangle A111536.

1, 3, 14, 84, 600, 4908, 44952, 454344, 5016768, 60062352, 775089312, 10728930912, 158638465536, 2496437377728, 41674737264000, 735831528563328, 13704461848753152, 268562085051533568, 5525005742876244480

Offset: 0

Author

Paul D. Hanna, Aug 06 2005

Keywords

• nonn

Crossrefs

Cf. A111536, A111541.

Programs

PARI

{a(n)=if(n<0,0,(matrix(n+3,n+3,m,j,if(m==j,1,if(m==j+1,-m+1, -(m-j-1)*polcoeff(log(sum(i=0,m,(i+1)!/1!*x^i)),m-j-1))))^-1)[n+3,3])}

Formula

a(n) = A111536(n+2, 2) = A111541(n+1, 0).