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A143122 Triangle read by rows, T(n,k) = Sum_{j=k..n} j!, 0 <= k <= n. 2
1, 2, 1, 4, 3, 2, 10, 9, 8, 6, 34, 33, 32, 30, 24, 154, 153, 152, 150, 144, 120, 874, 873, 872, 870, 864, 840, 720, 5914, 5913, 5912, 5910, 5904, 5880, 5760, 5040, 46234, 46233, 46232, 46230, 46224, 46200, 46080, 45360, 40320 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Left column = A003422 starting (1, 2, 4, 10, 34, ...).

Row sums = A007489 starting (1, 3, 9, 33, 153, ...).

LINKS

G. C. Greubel, Rows n = 0..100 of triangle, flattened

FORMULA

Triangle read by rows, T(n,k) = Sum_{j=k..n} j!, 0 <= k <= n. A000012 * (A000142 * 0^(n-k)) * A000012, where A000142 = (1, 1, 2, 6, ...).

EXAMPLE

First few rows of the triangle are:

   1;

   2,  1;

   4,  3,  2;

  10,  9,  8,  6;

  34, 33, 32, 30, 24;

  ...

T(4,2) = 32 = 4! + 3! + 2! = (24 + 6 + 2).

MAPLE

a:=proc(n, k) local j; add(factorial(j), j=k..n) end: seq(seq(a(n, k), k=0..n), n=0..8); # Muniru A Asiru, Oct 16 2018

MATHEMATICA

Table[Sum[j!, {j, k, n}], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Oct 15 2018 *)

PROG

(PARI) for(n=0, 15, for(k=0, n, print1(sum(j=k, n, j!), ", "))) \\ G. C. Greubel, Oct 15 2018

(MAGMA) [[(&+[Factorial(j): j in [k..n]]): k in [0..n]]: n in [0..10]]; // G. C. Greubel, Oct 15 2018

(GAP) Flat(List([0..8], n->List([0..n], k->Sum([k..n], j->Factorial(j))))); # Muniru A Asiru, Oct 16 2018

CROSSREFS

Cf. A000142, A003422, A007489.

Sequence in context: A140169 A124731 A210658 * A093067 A098122 A159931

Adjacent sequences:  A143119 A143120 A143121 * A143123 A143124 A143125

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson & Roger L. Bagula, Jul 26 2008

STATUS

approved

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Last modified November 18 11:26 EST 2018. Contains 317302 sequences. (Running on oeis4.)