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A123158 Square array related to Bell numbers read by antidiagonals. 4
1, 1, 1, 2, 2, 1, 5, 5, 3, 1, 15, 15, 10, 5, 1, 52, 52, 37, 22, 6, 1, 203, 203, 151, 99, 31, 9, 1, 877, 877, 674, 471, 160, 61, 10, 1, 4140, 4140, 3263, 2386, 856, 385, 75, 14, 1, 21147, 21147, 17007, 12867, 4802, 2416, 520, 135, 15, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

FORMULA

T(n,k)=0 if n<0, T(0,k)=1 for k>=0, T(n,k)=T(n,k-1)+1/2*(k+1)*T(n-1,k+1)if k is an odd number, T(n,k)=T(n,k-1)+T(n-1,k+1) if k is an even number . T(n,0)=A000110(n) ; T(n,1)=A000110(n+1) ; T(n,2)=A005493(n) ; T(n,3)=A033452(n) ; T(n,4)=A003128(n+2)

EXAMPLE

Square array begins:

1, 1, 1, 1, 1, ... (Row n=0 :A000012)

1, 2, 3, 5, 6, ... (Row n=1 :A117142)

2, 5, 10, 22, 31, ...

5, 15, 37, 99, 160, ...

15, 52, 151, 471, 856, ...

52, 203, 674, 2386, 4802, ...

MATHEMATICA

T[0, _?NonNegative] = 1;

T[n_, k_] := T[n, k] = If[n<0 || k<0, 0, If[OddQ[k], T[n, k-1] + (1/2)(k+1) T[n-1, k+1], T[n, k-1] + T[n-1, k+1]]];

Table[T[n-k, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Feb 21 2020 *)

CROSSREFS

Columns : A000110 (Bell numbers), A000110, A005493, A033452, A003128.

Rows : A000012, A117142.

Sequence in context: A271025 A134379 A108087 * A185414 A133611 A010094

Adjacent sequences:  A123155 A123156 A123157 * A123159 A123160 A123161

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Oct 01 2006

STATUS

approved

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Last modified October 25 14:22 EDT 2020. Contains 338012 sequences. (Running on oeis4.)