1,3

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

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

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,...).

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;

...

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 *)

Cf. A000670, A076726, A095989.

Sequence in context: A321477 A209998 A349972 * A389004 A364895 A299619

Adjacent sequences: A163201 A163202 A163203 * A163205 A163206 A163207

nonn,tabl,changed

Gary W. Adamson, Jul 23 2009

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

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

approved