A356651 Triangle read by rows. T(n, k) = [x^k](0^n + 4^n * ((1 - x)^(-1/2) - 1)).

1, 0, 2, 0, 8, 6, 0, 32, 24, 20, 0, 128, 96, 80, 70, 0, 512, 384, 320, 280, 252, 0, 2048, 1536, 1280, 1120, 1008, 924, 0, 8192, 6144, 5120, 4480, 4032, 3696, 3432, 0, 32768, 24576, 20480, 17920, 16128, 14784, 13728, 12870, 0, 131072, 98304, 81920, 71680, 64512, 59136, 54912, 51480, 48620

Offset

0,3

Links

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

Formula

T(n, 0) = 0^n, T(n, n) = binomial(2*n, n), otherwise T(n, k) = 4^(n - k)*T(k, k).

Example

[0] 1;
[1] 0,      2;
[2] 0,      8,     6;
[3] 0,     32,    24,    20;
[4] 0,    128,    96,    80,    70;
[5] 0,    512,   384,   320,   280,   252;
[6] 0,   2048,  1536,  1280,  1120,  1008,   924;
[7] 0,   8192,  6144,  5120,  4480,  4032,  3696,  3432;
[8] 0,  32768, 24576, 20480, 17920, 16128, 14784, 13728, 12870;
[9] 0, 131072, 98304, 81920, 71680, 64512, 59136, 54912, 51480, 48620;

Maple

ogf := n -> 0^n + 4^n * ((1 - x)^(-1/2) - 1):
ser := n -> series(ogf(n), x, 32):
seq(seq(coeff(ser(n), x, k), k = 0..n), n = 0..9);

Crossrefs

Cf. A000984, A004171, A172060 (row sums), A357012.

Sequence in context: A334071 A243406 A293934 * A316133 A359451 A243443

Adjacent sequences: A356648 A356649 A356650 * A356652 A356653 A356654

Keyword

nonn,tabl

Author

Peter Luschny, Sep 08 2022

Status

approved