login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 29 08:33 EST 2020. Contains 338762 sequences. (Running on oeis4.)