A046527 A triangle related to A000108 (Catalan) and A000302 (powers of 4).

1, 1, 1, 2, 5, 1, 5, 22, 9, 1, 14, 93, 58, 13, 1, 42, 386, 325, 110, 17, 1, 132, 1586, 1686, 765, 178, 21, 1, 429, 6476, 8330, 4746, 1477, 262, 25, 1, 1430, 26333, 39796, 27314, 10654, 2525, 362, 29, 1, 4862, 106762, 185517, 149052, 69930, 20754

Offset

0,4

Links

Table of n, a(n) for n=0..50.

Formula

a(n, m) = binomial(n, m-1)*(4^(n-m+1)-binomial(2*n, n)/binomial(2*(m-1), m-1))/2, n >= m >= 0. G.f. for column m: c(x)*(x/(1-4*x))^m, where c(x) = g.f. for Catalan numbers (A000108).

Crossrefs

The m=0..6 column sequences are: A000108, A000346, A018218, A042941, A042985, A045505, A045622. Row sums: A046814.

Sequence in context: A021803 A356273 A077382 * A008343 A257264 A093952

Adjacent sequences: A046524 A046525 A046526 * A046528 A046529 A046530

Keyword

easy,nonn,tabl

Author

Wolfdieter Lang

Status

approved