A156528 Triangle read by rows: T(n,m) = (-1)^n*Sum_{i=0..m} [(-1)^(m-i)*binomial(n- i-1, m-i)*Stirling_1(n+i+1,i+1), for 0 <= m <= n.

1, 1, 3, 2, 9, 35, 6, 38, 181, 735, 24, 202, 1148, 5395, 22449, 120, 1284, 8560, 45832, 213529, 902055, 720, 9468, 73052, 440516, 2275270, 10540509, 44990231, 5040, 79344, 700380, 4713740, 26783190, 135134070, 623527389, 2681453775, 40320

Offset

0,3

Comments

Row sums are {1, 4, 46, 960, 29218, 1171380, 58329766, 3472396928, 240584307106, 19018858710852, 1689457066042590, ...}. - see A191870.

Links

Table of n, a(n) for n=0..36.

Example

Triangle begins
{1},
{1, 3},
{2, 9, 35},
{6, 38, 181, 735},
{24, 202, 1148, 5395, 22449},
{120, 1284, 8560, 45832, 213529, 902055},
{720, 9468, 73052, 440516, 2275270, 10540509, 44990231},
{5040, 79344, 700380, 4713740, 26783190, 135134070, 623527389, 2681453775},
{40320, 744336, 7440840, 55477636, 344589972, 1883062894, 9345564224, 42994209331, 185953177553},
{362880, 7725600, 86678136, 711387192, 4804798156, 28306022216, 150469912896, 737690211448, 3386028203405, 14710753408923},
{3628800, 87884640, 1097845632, 9863244552, 72108611456, 456146630800, 2587934993000, 13476479586304, 65448246877514, 299870086199497, 1307535010540395}
For example, T(4,2) = 1148 = C(3,2)S1(5,1)-C(2,1)S1(6,2)+C(1,0)S1(7,3).

Mathematica

t[n_, m_] = (-1)^n*Sum[(-1)^(m - i)*Binomial[n - i - 1, m - i]*StirlingS1[n + i + 1, i + 1], {i, 0, m}];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Cf. A191870.

Sequence in context: A284989 A049971 A234748 * A234744 A092502 A292923

Adjacent sequences: A156525 A156526 A156527 * A156529 A156530 A156531

Keyword

nonn,tabl

Author

Roger L. Bagula, Feb 09 2009

Extensions

Corrected and edited by N. J. A. Sloane, Jun 18 2011

Status

approved