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A176242 A q-form recursion triangular sequence:q=2:t(n,k)=t(n - 1, k - 1) + q^k*t(n - 1, k). 0
1, 1, 1, 1, 5, 1, 1, 21, 13, 1, 1, 85, 125, 29, 1, 1, 341, 1085, 589, 61, 1, 1, 1365, 9021, 10509, 2541, 125, 1, 1, 5461, 73533, 177165, 91821, 10541, 253, 1, 1, 21845, 593725, 2908173, 3115437, 766445, 42925, 509, 1, 1, 87381, 4771645, 47124493, 102602157 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are:

{1, 2, 7, 36, 241, 2078, 23563, 358776, 7449061, 213188690,...}

REFERENCES

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

LINKS

Table of n, a(n) for n=1..50.

FORMULA

q=2:t(n,k)=t(n - 1, k - 1) + q^k*t(n - 1, k).

EXAMPLE

{1},

{1, 1},

{1, 5, 1},

{1, 21, 13, 1},

{1, 85, 125, 29, 1},

{1, 341, 1085, 589, 61, 1},

{1, 1365, 9021, 10509, 2541, 125, 1},

{1, 5461, 73533, 177165, 91821, 10541, 253, 1},

{1, 21845, 593725, 2908173, 3115437, 766445, 42925, 509, 1},

{1, 87381, 4771645, 47124493, 102602157, 52167917, 6260845, 173229, 1021, 1}

MATHEMATICA

Clear[A, n, k, q];

q = 2;

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: A047909 A171243 A111577 * A036969 A080249 A157154

Adjacent sequences:  A176239 A176240 A176241 * A176243 A176244 A176245

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Apr 12 2010

STATUS

approved

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Last modified April 26 04:11 EDT 2019. Contains 322469 sequences. (Running on oeis4.)