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 A067001 Triangle T(n,k) = d(n-k,n), 0 <= k <= n, where d(l,m) = Sum_{k=l..m} 2^k * binomial(2m-2k,m-k) * binomial(m+k,m) * binomial(k,l). 3

%I

%S 1,4,6,24,60,42,160,560,688,308,1120,5040,8760,7080,2310,8064,44352,

%T 99456,114576,68712,17556,59136,384384,1055040,1572480,1351840,642824,

%U 134596,439296,3294720,10695168,19536000,21778560,14912064,5864640,1038312

%N Triangle T(n,k) = d(n-k,n), 0 <= k <= n, where d(l,m) = Sum_{k=l..m} 2^k * binomial(2m-2k,m-k) * binomial(m+k,m) * binomial(k,l).

%H V. H. Moll, <a href="http://www.ams.org/notices/200203/fea-moll.pdf">The evaluation of integrals: a personal story</a>, Notices Amer. Math. Soc., 49 (No. 3, March 2002), 311-317.

%e Triangle starts:

%e 1;

%e 4, 6;

%e 24, 60, 42;

%e 160, 560, 688, 308;

%e 1120, 5040, 8760, 7080, 2310;

%e ...

%p d := proc(l,m) local k; add(2^k*binomial(2*m-2*k,m-k)*binomial(m+k,m)*binomial(k,l),k=l..m); end:

%p T:= (n, k)-> d(n-k, n):

%p seq(seq(T(n, k), k=0..n), n=0..10);

%o (PARI) d(l, m) = sum(kk=l, m, 2^kk*binomial(2*m-2*kk,m-kk)*binomial(m+kk,m)*binomial(kk,l));

%o tabl(nn) = {for (n=0, nn, for (k=0, n, print1(d(n-k, n), ", ");); print(););} \\ _Michel Marcus_, Jul 18 2015

%Y Column k=0 gives A059304.

%Y Row sums give A002458.

%Y Main diagonal gives A004982.

%K nonn,tabl

%O 0,2

%A _N. J. A. Sloane_, Feb 16 2002

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Last modified January 22 05:11 EST 2019. Contains 319353 sequences. (Running on oeis4.)