A153583 Convolution triangle by rows, A004736 * (A153582 * 0^(n-k)).

1, 2, 1, 3, 2, 3, 4, 3, 6, 9, 5, 4, 9, 18, 24, 6, 5, 12, 27, 48, 65, 7, 6, 15, 36, 72, 130, 177, 8, 7, 18, 45, 96, 195, 354, 481, 9, 8, 21, 54, 120, 260, 531, 962, 1308, 10, 9, 24, 63, 144, 325, 708, 1443, 2616, 3555, 11, 10, 27, 72, 168, 390, 885, 1924, 3924, 7110, 9664

Offset

0,2

Comments

Row sums = A024581: (1, 3, 8, 22, 60, 163,...).

Right border = A153582.

Links

Table of n, a(n) for n=0..65.

Steve Butler, R. L. Graham & Nan Zang, Jumping Sequences, Journal of Integer Sequences, Vol. 11, 2008, 08.4.5.

Formula

Convolution triangle by rows, A004736 * (A153582 * 0^(n-k)).

Example

First few rows of the triangle =
  1;
  2, 1;
  3, 2, 3;
  4, 3, 6, 9;
  5, 4, 9, 18, 24;
  6, 5, 12, 27, 48, 65;
  7, 6, 15, 36, 72, 130, 177;
  8, 7, 18, 45, 96, 195, 354, 481;
  9, 8, 21, 54, 120, 260, 531, 962, 1308;
  10, 9, 24, 63, 144, 325, 708, 1443, 2616, 3555;
  ...
Row 3 = (4, 3, 6, 9) = termwise products of (4, 3, 2, 1) and (1, 1, 3, 9);
where A153582 = (1, 1, 3, 9, 24, 65,...).

Prog

(PARI) tabl(nn) = {my(va = vector(nn), vc = vector(nn)); va[1] = 1; for (n=1, nn, if (n > 1, va[n] = round(exp(1)*va[n-1])); vc[n] = va[n] - sum(k=1, n-1, vc[k]*(n-k+1)); print(vector(n, k, vc[k]*(n-k+1))); ); } \\ Michel Marcus, Jan 28 2019

Crossrefs

Cf. A024581, A153582, A004736

Sequence in context: A133926 A144337 A143929 * A346797 A029163 A196191

Adjacent sequences: A153580 A153581 A153582 * A153584 A153585 A153586

Keyword

nonn,tabl

Author

Gary W. Adamson, Dec 28 2008

Extensions

More terms from Michel Marcus, Jan 28 2019

Status

approved