A113326 Table T(n,k), n>=1 and k>=0, read by antidiagonals, related to A111146.

1, 1, 1, 1, 2, 2, 1, 3, 8, 5, 1, 4, 18, 36, 15, 1, 5, 32, 117, 176, 54, 1, 6, 50, 272, 801, 928, 235, 1, 7, 72, 525, 2400, 5724, 5296, 1237, 1, 8, 98, 900, 5675, 21792, 42633, 33024, 7790, 1, 9, 128, 1421, 11520, 62650, 203008, 331911, 227776, 57581

Offset: 0

Author

Philippe Deléham and Paul D. Hanna, Oct 28 2005

Keywords

• nonn
• tabl

Examples

			Table begins:
1,1,2,5,15,54,235,1237,7790,57581, 489231, ...
1,2,8,36,176,928,5296,33024,227776,1757504, ...
1,3,18,117,801,5724,42633,331911,2717874,23620329, ...
1,4,32,272,2400,21792,203008,1940224,19065344,193410560, ...
1,5,50,525,5675,62650,703975,8042625,93454750,1106250125, ...
1,6,72,900,11520,149904,1976400,26363232,355648320, ...
1,7,98,1421,21021,315168,4774021,72945859,1123559906, ...
1,8,128,2112,35456,601984,10306048,177639936,3080264704, ...
1,9,162,2997,56295,1067742,20392803,391614669,7555447854, ...
1,10,200,4100,85200,1785600,37644400,797224000,16946456000,
...
		

Crossrefs

Cf. A111146, A051295 (row n=1), A113327 (row n=2), A113328 (row n=3), A113329 (row n=4), A113330 (row n=5), A113331 (row n=6).

Programs

PARI

{T(n,k)=local(y=Y+Y*O(Y^k)); polcoeff(1/(1-n/(n-1)!*y*sum(j=0,k,(n-1+j)!*y^j)),k,Y)}

Formula

T(n, k) = Sum_{j=0..k} n^j*A111146(k, j).

G.f. for row n: Sum_{k>=0}T(n, k)*y^k = 1/(1-n/(n-1)!*y*Sum_{j>=0}(n-1+j)!*y^j), for n>=1.