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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..54.

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

Adjacent sequences:  A113323 A113324 A113325 * A113327 A113328 A113329

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham and Paul D. Hanna, Oct 28 2005

STATUS

approved

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Last modified November 12 13:43 EST 2019. Contains 329058 sequences. (Running on oeis4.)