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A174640 A triangular sequence:t(n,m)=A033306(n,m)-A033306(n,0)+1 0
1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 6, 10, 6, 1, 1, 24, 49, 49, 24, 1, 1, 110, 248, 298, 248, 110, 1, 1, 545, 1308, 1749, 1749, 1308, 545, 1, 1, 2877, 7229, 10421, 11611, 10421, 7229, 2877, 1, 1, 16114, 41998, 64114, 77134, 77134, 64114, 41998, 16114, 1, 1, 95496 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Row sums are:

1, 2, 3, 6, 24, 148, 1016, 7206, 52667, 398722, 3137084,...

REFERENCES

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Combinatorics/BellNumber.nb.

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 80.

LINKS

Table of n, a(n) for n=0..56.

FORMULA

t(n,m)=A033306(n,m)-A033306(n,0)+1

EXAMPLE

{1},

{1, 1},

{1, 1, 1},

{1, 2, 2, 1},

{1, 6, 10, 6, 1},

{1, 24, 49, 49, 24, 1},

{1, 110, 248, 298, 248, 110, 1},

{1, 545, 1308, 1749, 1749, 1308, 545, 1},

{1, 2877, 7229, 10421, 11611, 10421, 7229, 2877, 1},

{1, 16114, 41998, 64114, 77134, 77134, 64114, 41998, 16114, 1},

{1, 95496, 256626, 410226, 523476, 565434, 523476, 410226, 256626, 95496, 1}

MATHEMATICA

b[0] := 1;

b[n_] := b[n] = Total[Table[b[k]Binomial[n - 1, k], {k, 0, n - 1}]];

a = b /@ Range[0, 70];

t[n_, m_] := Binomial[n, m]*a[[m + 1]]*a[[n - m + 1]];

Table[Table[t[n, m] - t[n, 0] + 1, {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

A033306

Sequence in context: A263755 A135879 A176224 * A138169 A139331 A173886

Adjacent sequences:  A174637 A174638 A174639 * A174641 A174642 A174643

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Mar 25 2010

STATUS

approved

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Last modified December 7 05:39 EST 2016. Contains 278841 sequences.