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A115082 Column 1 of triangle A115080. 6

%I

%S 1,2,5,20,94,507,3009,19350,132920,966962,7396366,59173897,492995320,

%T 4262193275,38125138575,351960913470,3346157796060,32700768584100,

%U 327957494280000,3370522049859990,35451669429671520,381183654441916290

%N Column 1 of triangle A115080.

%F a(n) = A115081(n) + n*A115081(n-1). - _Paul D. Hanna_, Feb 18 2007

%F 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

%o (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

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

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 13 2006

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)