A134135 Alternating row sums of triangle A134134.

1, 1, 5, 15, 93, 551, 4129, 33607, 312929, 3179343, 35602881, 432201743, 5678740945, 80142780751, 1210609725905, 19481112885231, 332836223507793, 6016678424942063, 114746996449871761, 2302527084416470255

Offset: 1

Author

Wolfdieter Lang Oct 12 2007

Keywords

• nonn
• easy

Comments

Difference of numbers sum(product(j!^e(n,m,k,j),j=1..n),k=1..p(n,m)) related to odd and even part m partitions of n. Here e(n,m,k,j) is the exponent of j in the k-th m part partition of n and p(n,m)=A008284(n,m) is the number of partitions of n with m parts.

Crossrefs

Cf. A077365 (row sums of A134134).

Formula

a(n)=sum(A134134(n,m)*(-1)^(m-1),m=1..n),n>=1.