A293724 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of e.g.f. exp(Sum_{j=1..k} j^2*x^j).

1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 9, 25, 1, 1, 1, 9, 79, 241, 1, 1, 1, 9, 79, 457, 1041, 1, 1, 1, 9, 79, 841, 5901, 10681, 1, 1, 1, 9, 79, 841, 7821, 66841, 60649, 1, 1, 1, 9, 79, 841, 10821, 118681, 720259, 658785, 1, 1, 1, 9, 79, 841, 10821, 136681, 1782019

Offset

0,9

Links

Seiichi Manyama, Antidiagonals n = 0..139, flattened

Formula

A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..min(k,n)} j^3*A(n-j,k)/(n-j)!.

Example

Square array begins:
   1,    1,    1,    1,     1, ...
   1,    1,    1,    1,     1, ...
   1,    9,    9,    9,     9, ...
   1,   25,   79,   79,    79, ...
   1,  241,  457,  841,   841, ...
   1, 1041, 5901, 7821, 10821, ...

Crossrefs

Columns k=1..4 give A000012, A293720, A293721, A293723.

Rows n=0-1 give A000012.

Main diagonal gives A255807.

Cf. A293669, A293718.

Sequence in context: A006084 A059928 A348049 * A283989 A361794 A361064

Adjacent sequences: A293721 A293722 A293723 * A293725 A293726 A293727

Keyword

nonn,tabl

Author

Seiichi Manyama, Oct 15 2017

Status

approved