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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
1, 4, 6, 24, 60, 42, 160, 560, 688, 308, 1120, 5040, 8760, 7080, 2310, 8064, 44352, 99456, 114576, 68712, 17556, 59136, 384384, 1055040, 1572480, 1351840, 642824, 134596, 439296, 3294720, 10695168, 19536000, 21778560, 14912064, 5864640, 1038312 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..35.

V. H. Moll, The evaluation of integrals: a personal story, Notices Amer. Math. Soc., 49 (No. 3, March 2002), 311-317.

EXAMPLE

Triangle starts:

1;

4, 6;

24, 60, 42;

160, 560, 688, 308;

1120, 5040, 8760, 7080, 2310;

...

MAPLE

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:

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

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

PROG

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

tabl(nn) = {for (n=0, nn, for (k=0, n, print1(d(n-k, n), ", "); ); print(); ); } \\ Michel Marcus, Jul 18 2015

CROSSREFS

Column k=0 gives A059304.

Row sums give A002458.

Main diagonal gives A004982.

Sequence in context: A283185 A034458 A240290 * A057343 A000287 A032087

Adjacent sequences:  A066998 A066999 A067000 * A067002 A067003 A067004

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Feb 16 2002

STATUS

approved

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Last modified December 13 12:49 EST 2018. Contains 318086 sequences. (Running on oeis4.)