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A176244 A q-form recursion triangular sequence:q=4:t(n,k)=t(n - 1, k - 1) + q^k*t(n - 1, k). 0
1, 1, 1, 1, 17, 1, 1, 273, 81, 1, 1, 4369, 5457, 337, 1, 1, 69905, 353617, 91729, 1361, 1, 1, 1118481, 22701393, 23836241, 1485393, 5457, 1, 1, 17895697, 1454007633, 6124779089, 1544878673, 23837265, 21841, 1, 1, 286331153, 93074384209 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are:

{1, 2, 19, 356, 10165, 516614, 49146967, 9165420200, 3350402793721,

2449781908163402,...}

REFERENCES

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

LINKS

Table of n, a(n) for n=1..39.

FORMULA

q=4:t(n,k)=t(n - 1, k - 1) + q^k*t(n - 1, k).

EXAMPLE

{1},

{1, 1},

{1, 17, 1},

{1, 273, 81, 1},

{1, 4369, 5457, 337, 1},

{1, 69905, 353617, 91729, 1361, 1},

{1, 1118481, 22701393, 23836241, 1485393, 5457, 1},

{1, 17895697, 1454007633, 6124779089, 1544878673, 23837265, 21841, 1},

{1, 286331153, 93074384209, 1569397454417, 1588080540241, 99182316113, 381680209, 87377, 1},

{1, 4581298449, 5957046920529, 401858822714961, 1627763870661201, 407838847339089, 6352630860369, 6108019281, 349521, 1}

MATHEMATICA

Clear[A, n, k, q];

q = 4;

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: A144442 A157151 A176794 * A022180 A156581 A015143

Adjacent sequences:  A176241 A176242 A176243 * A176245 A176246 A176247

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Apr 12 2010

STATUS

approved

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Last modified April 23 18:06 EDT 2019. Contains 322387 sequences. (Running on oeis4.)