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A113326
Table T(n,k), n>=1 and k>=0, read by antidiagonals, related to A111146.
6
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
0,5
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.
EXAMPLE
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,
...
PROG
(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)}
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).
Sequence in context: A059584 A295736 A136203 * A262157 A090447 A241186
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved