A162498 Triangle read by rows: T(n,k) = Sum[(-1)^j Binomial[n, j](k + 1 - j)^(n - 1), {j, 0, k}].

1, 1, 1, 3, 4, 1, 23, 33, 11, 1, 425, 620, 220, 26, 1, 18129, 26525, 9520, 1180, 57, 1, 1721419, 2519664, 905765, 113050, 5649, 120, 1, 353654167, 517670461, 186123259, 23248085, 1166221, 25347, 247, 1, 153923102577, 225309742552, 81009042744

Offset

1,4

Comments

Row sums are: {1, 2, 8, 68, 1292, 55412, 5265668, 1081887788, 470880100412, 427569972956852, 800992247015505668,...}.

Links

Table of n, a(n) for n=1..39.

Example

{1},
{1, 1},
{3, 4, 1},
{23, 33, 11, 1},
{425, 620, 220, 26, 1},
{18129, 26525, 9520, 1180, 57, 1},
{1721419, 2519664, 905765, 113050, 5649, 120, 1},
{353654167, 517670461, 186123259, 23248085, 1166221, 25347, 247, 1},
{153923102577, 225309742552, 81009042744, 10119247684, 507795498, 11059468, 109386, 502, 1},
{139765654884545, 204586385695065, 73558129319520, 9188556369384, 461102826618, 10043953290, 99446730, 460686, 1013, 1},
{261831303051976691, 383263833094891100, 137800821538668585, 17213473445481060, 863812603482906, 18816103842228, 186311714820, 863536410, 1909831, 2036, 1} (End)

Mathematica

t[n_, k_]:=Sum[(-1)^j Binomial[n, j](k+1-j)^(n-1), {j, 0, k}];
M[n_]:=Table[If[k <= m, (-1)^(m+k)*t[m, k], 0], {k, 0, n-2}, {m, 2, n}]; Flatten[Table[Table[Inverse[M[12]][[m, n]], {m, 1, n}], {n, 1, 11}]]

Crossrefs

Cf. A154921. An unsigned version of A055325.

Sequence in context: A354293 A255905 A055325 * A134049 A224069 A157783

Adjacent sequences: A162495 A162496 A162497 * A162499 A162500 A162501

Keyword

nonn,easy,tabl

Author

Roger L. Bagula and Mats Granvik, Dec 06 2009

Status

approved