A115082 Column 1 of triangle A115080.

1, 2, 5, 20, 94, 507, 3009, 19350, 132920, 966962, 7396366, 59173897, 492995320, 4262193275, 38125138575, 351960913470, 3346157796060, 32700768584100, 327957494280000, 3370522049859990, 35451669429671520, 381183654441916290

Offset: 0

Author

Paul D. Hanna, Jan 13 2006

Keywords

• nonn

Crossrefs

Cf. A115080, A115081 (column 0), A115083 (column 2), A115084 (row sums); A115087.

Cf. A000108.

Programs

PARI

{a(n)=sum(k=0,(n+1)\2,binomial(2*n-2*k,n-k)/(n-k+1)*binomial(2*k,k)/(k+1) *(k+1)!*binomial(n+1,2*k)/2^k)} \\ Paul D. Hanna, Feb 18 2007

Formula

From Paul D. Hanna, Feb 18 2007: (Start)

a(n) = A115081(n) + n*A115081(n-1).

a(n) = Sum_{k=0..[(n+1)/2]} A000108(n-k)*A000108(k)*(k+1)!*C(n+1,2*k)/2^k, where A000108(n) = C(2*n,n)/(n+1) is the n-th Catalan number. (End)