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A262886
Regular triangle read by rows: T(n, k) = sum(i=0, n, sum(j=k, n, 3*(-1)^(k+j)*binomial(2*k,k)*binomial(j,i)*binomial(n,i)*binomial(i,n-j)/(2*(2*i-1)*(2*j+1)*(2*n-2*i-1)))).
0
-2, 0, 6, 0, 0, 24, 0, 0, 4, 118, 0, 0, 0, 60, 696, 0, 0, 0, 12, 720, 4824, 0, 0, 0, 0, 336, 8288, 38240, 0, 0, 0, 0, 60, 6516, 95928, 336822, 0, 0, 0, 0, 0, 2520, 109872, 1131732, 3215544, 0, 0, 0, 0, 0, 392, 67904, 1735320, 13647840, 32651544
OFFSET
1,1
FORMULA
T(0, 0) = 3/2, so sequence here as offset 1.
T(n, k) = 0 for k>n, so only the terms with k<=n are represented here.
EXAMPLE
Triangle starts:
-2;
0, 6;
0, 0, 24;
0, 0, 4, 118;
0, 0, 0, 60, 696;
0, 0, 0, 12, 720, 4824;
0, 0, 0, 0, 336, 8288, 38240;
0, 0, 0, 0, 60, 6516, 95928, 336822;
...
MATHEMATICA
Table[Sum[Sum[3 (-1)^(k + j) Binomial[2 k, k] Binomial[j, i] Binomial[n, i] Binomial[i, n - j]/(2 (2 i - 1) (2 j + 1) (2 n - 2 i - 1)), {j, k, n}], {i, 0, n}], {n, 10}, {k, n}] // Flatten (* Michael De Vlieger, Oct 04 2015 *)
PROG
(PARI) d(n, k) = sum(i=0, n, sum(j=k, n, 3*(-1)^(k+j)*binomial(2*k, k)*binomial(j, i)*binomial(n, i)*binomial(i, n-j)/(2*(2*i-1)*(2*j+1)*(2*n-2*i-1))));
tabl(nn) = {for (n=1, nn, for (k=1, n, print1(d(n, k), ", "); ); print(); ); }
CROSSREFS
Sequence in context: A047918 A321981 A322481 * A138701 A332400 A355143
KEYWORD
sign,tabl
AUTHOR
Michel Marcus, Oct 04 2015
STATUS
approved