A246381 Triangular matrix T defined by T = exp(L) where L(n,k) = C(2*n, 2*k+1)/2, as read by rows n >= 0, k=0..n.

1, 1, 1, 3, 2, 1, 12, 13, 3, 1, 73, 80, 34, 4, 1, 584, 701, 296, 70, 5, 1, 5889, 7680, 3463, 816, 125, 6, 1, 73184, 100519, 49432, 12139, 1876, 203, 7, 1, 1089057, 1571040, 810268, 217728, 34294, 3808, 308, 8, 1, 19019632, 28717865, 15455072, 4354260, 751792, 83406, 7056, 444, 9, 1

Offset

0,4

Links

Table of n, a(n) for n=0..54.

Example

Triangle begins:
1;
1, 1;
3, 2, 1;
12, 13, 3, 1;
73, 80, 34, 4, 1;
584, 701, 296, 70, 5, 1;
5889, 7680, 3463, 816, 125, 6, 1;
73184, 100519, 49432, 12139, 1876, 203, 7, 1;
1089057, 1571040, 810268, 217728, 34294, 3808, 308, 8, 1;
19019632, 28717865, 15455072, 4354260, 751792, 83406, 7056, 444, 9, 1;
384301729, 603257920, 338772685, 99130208, 17974226, 2186368, 181602, 12192, 615, 10, 1; ...
The matrix logarithm, L, begins:
0;
1, 0;
2, 2, 0;
3, 10, 3, 0;
4, 28, 28, 4, 0;
5, 60, 126, 60, 5, 0;
6, 110, 396, 396, 110, 6, 0;
7, 182, 1001, 1716, 1001, 182, 7, 0;
8, 280, 2184, 5720, 5720, 2184, 280, 8, 0;
9, 408, 4284, 15912, 24310, 15912, 4284, 408, 9, 0;
10, 570, 7752, 38760, 83980, 83980, 38760, 7752, 570, 10, 0; ...
where L(n,k) = C(2*n, 2*k+1)/2.
The matrix square begins:
1;
2, 1;
8, 4, 1;
46, 32, 6, 1;
376, 280, 80, 8, 1;
3962, 3304, 972, 160, 10, 1;
52268, 47100, 15400, 2552, 280, 12, 1;
837574, 803852, 283394, 51704, 5642, 448, 14, 1;
15919312, 16175600, 6028944, 1187632, 141136, 11088, 672, 16, 1; ...

Prog

(PARI) {T(n, k)=local(L=matrix(n+1, n+1, r, c, if(r>=c, binomial(2*r-2, 2*c-1)/2)), A);
A=sum(m=0, n, L^m/m!); A[n+1, k+1]}
for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))

Crossrefs

Cf. A246382, A246383, A246384, A246385, A246386, A246387.

Sequence in context: A213262 A280512 A068440 * A048647 A358310 A180190

Adjacent sequences: A246378 A246379 A246380 * A246382 A246383 A246384

Keyword

nonn,tabl

Author

Paul D. Hanna, Aug 24 2014

Status

approved