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A163204 Triangle read by rows, A095989 convolved with A000670. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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: A057761 A321477 A209998 * A299619 A215269 A336246

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

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Last modified October 17 13:24 EDT 2021. Contains 348049 sequences. (Running on oeis4.)