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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). 6
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 (list; table; graph; refs; listen; history; text; internal format)
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 A322029 A322107

Adjacent sequences:  A293721 A293722 A293723 * A293725 A293726 A293727

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, Oct 15 2017

STATUS

approved

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Last modified October 21 14:42 EDT 2021. Contains 348155 sequences. (Running on oeis4.)