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A176243 A q-form recursion triangular sequence:q=3:t(n,k)=t(n - 1, k - 1) + q^k*t(n - 1, k). 0
1, 1, 1, 1, 10, 1, 1, 91, 37, 1, 1, 820, 1090, 118, 1, 1, 7381, 30250, 10648, 361, 1, 1, 66430, 824131, 892738, 98371, 1090, 1, 1, 597871, 22317967, 73135909, 24796891, 892981, 3277, 1, 1, 5380840, 603182980, 5946326596, 6098780422, 675780040 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are:

{1, 2, 12, 130, 2030, 48642, 1882762, 121744898, 13337520498, 2503662940162,...}

REFERENCES

Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), page 176

LINKS

Table of n, a(n) for n=1..42.

FORMULA

q=3:t(n,k)=t(n - 1, k - 1) + q^k*t(n - 1, k).

EXAMPLE

{1},

{1, 1},

{1, 10, 1},

{1, 91, 37, 1},

{1, 820, 1090, 118, 1},

{1, 7381, 30250, 10648, 361, 1},

{1, 66430, 824131, 892738, 98371, 1090, 1},

{1, 597871, 22317967, 73135909, 24796891, 892981, 3277, 1},

{1, 5380840, 603182980, 5946326596, 6098780422, 675780040, 8059780, 9838, 1},

{1, 48427561, 16291321300, 482255637256, 1487949969142, 498742429582, 18302518900, 72606898, 29521, 1}

MATHEMATICA

Clear[A, n, k, q];

q = 3;

A[n_, 1] := 1;

A[n_, n_] := 1;

A[n_, k_] := A[n, k] = A[n - 1, k - 1] + q^k*A[n - 1, k];

a = Table[A[n, k], {n, 1, 10}, {k, 1, n}];

Flatten[a]

CROSSREFS

Sequence in context: A176021 A166972 A160562 * A022173 A158117 A172378

Adjacent sequences:  A176240 A176241 A176242 * A176244 A176245 A176246

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Apr 12 2010

STATUS

approved

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Last modified April 19 09:10 EDT 2019. Contains 322241 sequences. (Running on oeis4.)