A370382 - OEIS

A370382

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

1, 1, 2, 1, 5, 7, 1, 13, 27, 34, 1, 33, 108, 176, 210, 1, 81, 437, 944, 1364, 1574, 1, 193, 1758, 5154, 9144, 12292, 13866, 1, 449, 6959, 28304, 62496, 98742, 126474, 140340, 1, 1025, 26988, 155034, 431644, 808564, 1183264, 1463944, 1604284, 1, 2305, 102473, 841960, 2992648, 6703438, 11276398, 15626632, 18835200, 20439484

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

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

FORMULA

Conjecture: A(n,0) = A249833(n+1). - Mikhail Kurkov, Apr 25 2024

EXAMPLE

Array begins:

=================================================

n\k| 0 1 2 3 4 5 ...

---+---------------------------------------------

0 | 1 1 1 1 1 1 ...

1 | 2 5 13 33 81 193 ...

2 | 7 27 108 437 1758 6959 ...

3 | 34 176 944 5154 28304 155034 ...

4 | 210 1364 9144 62496 431644 2992648 ...

5 | 1574 12292 98742 808564 6703438 55967104 ...

...

PROG

(PARI)

A(m, n=m)={my(r=vectorv(m+1), v=vector(n+m+1, k, 1)); r[1] = v[1..n+1];

for(i=1, m, v=vector(#v-1, k, v[k+1] + k*sum(j=1, k, binomial(k-1, j-1)*v[j])); r[1+i] = v[1..n+1]); Mat(r)}

{ A(5) }

CROSSREFS

Cf. A249833.

Sequence in context: A193630 A144505 A369527 * A059039 A332022 A109261

Adjacent sequences: A370379 A370380 A370381 * A370383 A370384 A370385

KEYWORD

nonn,tabl,changed

AUTHOR

Mikhail Kurkov, Feb 17 2024

STATUS

approved