A163204 Triangle read by rows, A095989 convolved with A000670.

1, 1, 2, 3, 2, 8, 13, 6, 8, 48, 75, 26, 24, 48, 368, 541, 150, 104, 144, 368, 3376, 4683, 1082, 600, 624, 1104, 3376, 35824, 47293, 9366, 4328, 3600, 4784, 10128, 35824, 430512, 545835, 94586, 37464, 25968, 27600, 43888, 107472, 430512, 5773936, 7087261, 1091670, 378344, 224784, 199088, 253200, 465712, 1291536, 5773936, 85482032

Offset

1,3

Comments

Row sums = A000670 starting with offset 1: (1, 3, 13, 75, 541, 4683,...).

Left border = A000670, right border = A095989.

Second column: A076726. - Michel Marcus, Mar 31 2016

Links

G. C. Greubel, Table of n, a(n) for n = 1..1225

Formula

Descending antidiagonals of a multiplication table formed by convolving A095989 with A000670, where A095989 is the INVERTi transform of A000670 starting (1, 3, 13, 75,...).

Example

First few rows of the triangle are:
1;
1, 2;
3, 2, 8;
13, 6, 8, 48;
75, 26, 24, 48, 368;
541, 150, 104, 144, 368, 3376;
4683, 1082, 600, 624, 1104, 3376, 35824;
47293, 9366, 4328, 3600, 4784, 10128, 35824, 430512;
...

Mathematica

max = 10; Fubini[n_, r_] := Sum[k!*Sum[(-1)^(i+k+r)*(i+r)^(n-r)/(i!*(k - i - r)!), {i, 0, k - r}], {k, r, n}]; Fubini[0, 1] = 1; A000670 = Table[ Fubini[n, 1], {n, 0, max}]; s = 1 - 1/Sum[Fubini[k, 1] q^k, {k, 0, max}] + O[q]^max; A095989 = CoefficientList[s/q, q]; row[n_] := A095989[[1 ;; n]]*Reverse[A000670[[1 ;; n]]]; Table[row[n], {n, 1, max-1}] // Flatten (* Jean-François Alcover, Mar 31 2016 *)

Crossrefs

Cf. A000670, A076726, A095989.

Sequence in context: A321477 A209998 A349972 * A364895 A299619 A215269

Adjacent sequences: A163201 A163202 A163203 * A163205 A163206 A163207

Keyword

nonn,tabl

Author

Gary W. Adamson, Jul 23 2009

Extensions

a(23) corrected by Jean-François Alcover, Mar 31 2016

Terms a(37) onward added by G. C. Greubel, Dec 10 2016

Status

approved