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A155826 A triangular sequence: t(n,m)=(Binomial[n, m] + Binomial[m*(n - m), n] + 2*((-1)^(n - 2*m)*StirlingS1[n, m]StirlingS1[n, n - m])). 0
1, 1, 1, 4, 1, 1, 15, 15, 1, 1, 76, 249, 76, 1, 1, 485, 3516, 3516, 485, 1, 1, 3606, 46623, 101354, 46623, 3606, 1, 1, 30247, 617541, 2388107, 2388107, 617541, 30247, 1, 1, 282248, 8416315, 51483931, 91651662, 51483931, 8416315, 282248, 1, 1, 2903049 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row sums are:

{4, 2, 6, 32, 403, 8004, 201814, 6071792, 212016652, 8430651132, 376203306434,...}

LINKS

Table of n, a(n) for n=0..45.

FORMULA

t(n,m)=(Binomial[n, m] + Binomial[m*(n - m), n] + 2*((-1)^(n - 2*m)*StirlingS1[n, m]StirlingS1[n, n - m])).

EXAMPLE

{4},

{1, 1},

{1, 4, 1},

{1, 15, 15, 1},

{1, 76, 249, 76, 1},

{1, 485, 3516, 3516, 485, 1},

{1, 3606, 46623, 101354, 46623, 3606, 1},

{1, 30247, 617541, 2388107, 2388107, 617541, 30247, 1},

{1, 282248, 8416315, 51483931, 91651662, 51483931, 8416315, 282248, 1},

{1, 2903049, 119667766, 1071669632, 3021085118, 3021085118, 1071669632, 119667766, 2903049, 1},

{1, 32659210, 1786250293, 22164382836, 91580770746, 145075180262, 91580770746, 22164382836, 1786250293, 32659210, 1}

MATHEMATICA

t[n_, m_] = (Binomial[n, m] + Binomial[m*(n - m), n] + 2*((-1)^(n - 2*m)*StirlingS1[n, m]StirlingS1[n, n - m]));

Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A176428 A116469 A156599 * A010320 A152571 A008304

Adjacent sequences:  A155823 A155824 A155825 * A155827 A155828 A155829

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Jan 28 2009

STATUS

approved

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Last modified May 25 01:17 EDT 2019. Contains 323534 sequences. (Running on oeis4.)