A379459 Array read by downward antidiagonals: A(n,k) = A(n-1,k+1) + 2*(k+1)!*Sum_{j=0..k} A(n-1,j)/j! with A(0,k) = 2*(k+1)!, n >= 0, k >= 0.

2, 4, 8, 12, 36, 52, 48, 192, 368, 472, 240, 1200, 2880, 4560, 5504, 1440, 8640, 24960, 47280, 67408, 78416, 10080, 70560, 238560, 527520, 871584, 1163232, 1320064, 80640, 645120, 2499840, 6330240, 11926656, 18031104, 22997696, 25637824, 725760, 6531840, 28546560, 81527040, 172811520, 292642560, 415728960, 513000000, 564275648

Offset

0,1

Links

Table of n, a(n) for n=0..44.

Formula

Conjecture: A(n,0) = A006351(n+2).

Example

Array begins:
================================================================
n\k|     0       1        2         3          4           5 ...
---+------------------------------------------------------------
0  |     2       4       12        48        240        1440 ...
1  |     8      36      192      1200       8640       70560 ...
2  |    52     368     2880     24960     238560     2499840 ...
3  |   472    4560    47280    527520    6330240    81527040 ...
4  |  5504   67408   871584  11926656  172811520  2649749760 ...
5  | 78416 1163232 18031104 292642560 4977020160 88700451840 ...
  ...

Prog

(PARI) A(m, n=m)={my(r=vectorv(m+1), v=vector(n+m+1, k, 2*k!)); r[1] = v[1..n+1];
for(i=1, m, v=vector(#v-1, k, v[k+1] + 2*k!*sum(j=1, k, v[j]/(j-1)!)); r[1+i] = v[1..n+1]); Mat(r)}
{ A(5) }

Crossrefs

Cf. A006351.

Sequence in context: A202148 A215825 A177268 * A289085 A242924 A133802

Adjacent sequences: A379456 A379457 A379458 * A379460 A379461 A379462

Keyword

nonn,tabl

Author

Mikhail Kurkov, Dec 23 2024

Status

approved