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A115082 Column 1 of triangle A115080. 6
1, 2, 5, 20, 94, 507, 3009, 19350, 132920, 966962, 7396366, 59173897, 492995320, 4262193275, 38125138575, 351960913470, 3346157796060, 32700768584100, 327957494280000, 3370522049859990, 35451669429671520, 381183654441916290 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

a(n) = A115081(n) + n*A115081(n-1). - Paul D. Hanna, Feb 18 2007

a(n) = Sum_{k=0..[(n+1)/2]} A000108(n-k)*A000108(k)*(k+1)!*C(n+1,2k)/2^k), where A000108(n) = C(2n,n)/(n+1) is the n-th Catalan number. - Paul D. Hanna, Feb 18 2007

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.

Sequence in context: A002484 A280102 A277686 * A020105 A214816 A020005

Adjacent sequences:  A115079 A115080 A115081 * A115083 A115084 A115085

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 13 2006

STATUS

approved

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Last modified August 1 03:52 EDT 2021. Contains 346384 sequences. (Running on oeis4.)