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

0,2

Links

Table of n, a(n) for n=0..21.

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)

Prog

(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

Crossrefs

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

Cf. A000108.

Sequence in context: A280102 A366452 A277686 * A020105 A347071 A214816

Adjacent sequences: A115079 A115080 A115081 * A115083 A115084 A115085

Keyword

nonn

Author

Paul D. Hanna, Jan 13 2006

Status

approved