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A144374 Triangle T(n,k), n>=1, 1<=k<=n, read by rows, where sequence a_k of column k begins with (k+1) 1's and a_k(n) shifts k places down under Dirichlet convolution. 9
1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 9, 2, 2, 1, 1, 18, 5, 2, 2, 1, 1, 40, 4, 3, 2, 2, 1, 1, 80, 12, 4, 3, 2, 2, 1, 1, 168, 8, 6, 2, 3, 2, 2, 1, 1, 340, 28, 6, 6, 2, 3, 2, 2, 1, 1, 698, 17, 10, 4, 4, 2, 3, 2, 2, 1, 1, 1396, 60, 13, 8, 4, 4, 2, 3, 2, 2, 1, 1, 2844, 34, 16, 5, 6, 2, 4, 2, 3, 2, 2, 1, 1, 5688 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Sequence a_k of column k begins with k terms from A000012 (only the last is in the triangle), followed by the first (k+1) terms from A000005.

LINKS

Alois P. Heinz, Rows n = 1..141, flattened

N. J. A. Sloane, Transforms

EXAMPLE

Triangle begins:

   1;

   1,  1;

   2,  1, 1;

   4,  2, 1, 1;

   9,  2, 2, 1, 1;

  18,  5, 2, 2, 1, 1;

MAPLE

with(numtheory): dck:= proc(b, c) proc(n, k) option remember; add(b(d, k) *c(n/d, k), d=`if`(n<0, {}, divisors(n))) end end: B:= dck(T, T): T:= (n, k)-> if n<=k then 1 else B(n-k, k) fi: seq(seq(T(n, k), k=1..n), n=1..14);

MATHEMATICA

dck[b_, c_][n_, k_] := dck[b, c][n, k] = Sum[b[d, k]*c[n/d, k], {d, If[n < 0, {}, Divisors[n]]}]; B = dck[T, T]; T[n_, k_] := If[n <= k, 1, B[n-k, k]]; Table[Table[T[n, k], {k, 1, n}], {n, 1, 14}] // Flatten (* Jean-François Alcover, Jan 15 2014, translated from Maple *)

CROSSREFS

Columns 1-9 give: A038044, A144366, A144367, A144368, A144369, A144370, A144371, A144372, A144373.

Cf. A000012, A000005.

Sequence in context: A098050 A278984 A111579 * A144018 A258709 A239144

Adjacent sequences:  A144371 A144372 A144373 * A144375 A144376 A144377

KEYWORD

eigen,nonn,tabl

AUTHOR

Alois P. Heinz, Sep 18 2008

STATUS

approved

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Last modified May 9 04:55 EDT 2021. Contains 343687 sequences. (Running on oeis4.)