A392037 Square table read by downward antidiagonals: n-th row has e.g.f. (1-9*x)^(-n/9).

1, 0, 1, 0, 1, 1, 0, 10, 2, 1, 0, 190, 22, 3, 1, 0, 5320, 440, 36, 4, 1, 0, 196840, 12760, 756, 52, 5, 1, 0, 9054640, 484880, 22680, 1144, 70, 6, 1, 0, 498005200, 22789360, 884520, 35464, 1610, 90, 7, 1, 0, 31872332800, 1276204160, 42456960, 1418560, 51520, 2160, 112, 8, 1

Offset

0,8

Links

Table of n, a(n) for n=0..54.

Formula

T(n,0) = 1; T(n,k) = Product_{i=0..k-1} (9*i+n).

T(n,k) = 9^(k-1)*n*Pochhammer(1+n/9,k-1). - Stefano Spezia, Dec 29 2025

Example

Rows 1..10:
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
1, 1, 10, 190, 5320, 196840, 9054640, 498005200, 31872332800, 2326680294400, 190787784140800, ...
1, 2, 22, 440, 12760, 484880, 22789360, 1276204160, 82953270400, 6138542009600, 509498986796800, ...
1, 3, 36, 756, 22680, 884520, 42456960, 2420046720, 159723083520, 11979231264000, 1006255426176000, ...
1, 4, 52, 1144, 35464, 1418560, 69509440, 4031547520, 270113683840, 20528639971840, 1744934397606400, ...
1, 5, 70, 1610, 51520, 2112320, 105616000, 6231344000, 423731392000, 32627317184000, 2805949277824000, ...
1, 6, 90, 2160, 71280, 2993760, 152681760, 9160905600, 632102486400, 49303993939200, 4289447472710400, ...
1, 7, 112, 2800, 95200, 4093600, 212867200, 12984899200, 908942944000, 71806492576000, 6318971346688000, ...
1, 8, 136, 3536, 123760, 5445440, 288608320, 17893715840, 1270453824640, 101636305971200, 9045631231436800, ...
1, 9, 162, 4374, 157464, 7085880, 382637520, 24106163760, 1735643790720, 140587147048320, 12652843234348800, ...
1, 10, 190, 5320, 196840, 9054640, 498005200, 31872332800, 2326680294400, 190787784140800, 17361688356812800, ...

Prog

(PARI) T(n, k) = prod(i=0, k-1, 9*i+n)

Crossrefs

Rows 1-19: A045756, A084949, A144758, A144829, A147629, A147630, A147631, A049211, A051232, A045756, A035012, A035013, A035017, A035018, A035020, A035021, A035022, A035023, A053116.

Sequence in context: A071938 A261942 A359734 * A057603 A040097 A010174

Adjacent sequences: A392034 A392035 A392036 * A392038 A392039 A392040

Keyword

nonn,easy,tabl

Author

Jianing Song, Dec 29 2025

Status

approved