A141028 A triangular sequence of the expansion of: (1-Prime[n])^n: t(n,m)=(-1)^m*Prime[n]^(n - m)*Binomial[n, m]; with Prime[0]=1 defined to extend and lower the results.

1, 2, -1, 9, -6, 1, 125, -75, 15, -1, 2401, -1372, 294, -28, 1, 161051, -73205, 13310, -1210, 55, -1, 4826809, -2227758, 428415, -43940, 2535, -78, 1, 410338673, -168962983, 29816997, -2923235, 171955, -6069, 119, -1, 16983563041, -7150973912, 1317284668, -138661544, 9122470, -384104

Offset

1,2

Comments

Row sums are:

{1, 1, 4, 64, 1296, 100000, 2985984, 268435456, 11019960576, 1207269217792,

296196766695424}

Links

Table of n, a(n) for n=1..42.

Formula

t(n,m)=(-1)^m*Prime[n]^(n - m)*Binomial[n, m].

Example

{1},
{2, -1},
{9, -6, 1},
{125, -75,15, -1},
{2401, -1372, 294, -28, 1},
{161051, -73205, 13310, -1210,55, -1},
{4826809, -2227758, 428415, -43940, 2535, -78, 1},
{410338673, -168962983, 29816997, -2923235, 171955, -6069, 119, -1},
{16983563041, -7150973912, 1317284668, -138661544,9122470, -384104, 10108, -152, 1},
{1801152661463, -704798867529, 122573716092, -12435014676, 810979218, -35259966, 1022028, -19044, 207, -1},
{420707233300201, -145071459758690, 22511088583245, -2069985157080, 124912897410, -5168809548, 148529010, -2926680, 37845, -290, 1}

Mathematica

Clear[T, n, m] T[n_, m_] = If[n == 0, (-1)^m*Binomial[n, m], (-1)^m*Prime[n]^(n - m)*Binomial[n, m]]; a = Table[Table[T[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[a]

Crossrefs

Sequence in context: A061691 A235595 A061356 * A246323 A201685 A120671

Adjacent sequences: A141025 A141026 A141027 * A141029 A141030 A141031

Keyword

uned,tabl,sign

Author

Roger L. Bagula, Jul 29 2008

Status

approved