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A156788 Triangle read by rows:A000166:a(n)= n*a(n - 1) + (-1)^n; t(n,m)=If[n == 0, 1, Binomial[n, m]*a(n - m )*m^n]. 0
1, 0, 1, 0, 0, 4, 0, 3, 0, 27, 0, 8, 96, 0, 256, 0, 45, 640, 2430, 0, 3125, 0, 264, 8640, 29160, 61440, 0, 46656, 0, 1855, 118272, 688905, 1146880, 1640625, 0, 823543, 0, 14832, 1899520, 16166304, 41287680, 43750000, 47029248, 0, 16777216, 0, 133497 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Row sums are: A137341;

{1, 1, 4, 30, 360, 6240, 146160, 4420080, 166924800, 7673823360, 420850080000,...}.

REFERENCES

J. Riordan, Combinatorial Identities, Wiley, 1968, p.194.

LINKS

Table of n, a(n) for n=0..46.

FORMULA

a(n)= n*a(n - 1) + (-1)^n;

t(n,m)=If[n == 0, 1, Binomial[n, m]*a(n - m )*m^n].

EXAMPLE

{1},

{0, 1},

{0, 0, 4},

{0, 3, 0, 27},

{0, 8, 96, 0, 256},

{0, 45, 640, 2430, 0, 3125},

{0, 264, 8640, 29160, 61440, 0, 46656},

{0, 1855, 118272, 688905, 1146880, 1640625, 0, 823543},

{0, 14832, 1899520, 16166304, 41287680, 43750000, 47029248, 0, 16777216},

{0, 133497, 34172928, 438143580, 1453326336, 2214843750, 1693052928, 1452729852, 0, 387420489},

{0, 1334960, 683504640, 13137221520, 58353254400, 108281250000, 114281072640, 67794059760, 48318382080, 0, 10000000000}

MATHEMATICA

a[0] = 1;

a[n_] := n*a[n - 1] + (-1)^n;

d = Table[a[n], {n, 0, 30}];

t[n_, m_] = If[n == 0, 1, Binomial[n, m]*d[[n - m + 1]]*m^n];

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

Flatten[%]

CROSSREFS

Cf. A000166, A137341.

Sequence in context: A290328 A200682 A263618 * A130801 A280579 A086165

Adjacent sequences:  A156785 A156786 A156787 * A156789 A156790 A156791

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 15 2009

STATUS

approved

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Last modified August 11 00:32 EDT 2020. Contains 336403 sequences. (Running on oeis4.)