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A099759 Triangle read by rows: T(n,0)=1, T(n,n)=1, T(n, k) = 2*(n-k)*T(n-1, k-1) + 2*k*T(n-1, k). 2
1, 1, 1, 1, 4, 1, 1, 12, 12, 1, 1, 30, 96, 30, 1, 1, 68, 564, 564, 68, 1, 1, 146, 2800, 6768, 2800, 146, 1, 1, 304, 12660, 63008, 63008, 12660, 304, 1, 1, 622, 54288, 504648, 1008128, 504648, 54288, 622, 1, 1, 1260, 225860, 3679344, 13111504, 13111504, 3679344, 225860, 1260, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

G. C. Greubel, Rows n = 0..100 of triangle, flattened

FORMULA

Sum_{k=0..n} T(n, k) = 2*(n-1)*(Sum_{k=0..n-1} T(n-1, k)) + 2 = A099760(n).

EXAMPLE

Triangle begins:

  1;

  1,  1;

  1,  4,   1;

  1, 12,  12,   1;

  1, 30,  96,  30,  1;

  1, 68, 564, 564, 68, 1;

MAPLE

T:=proc(n, k) if k=0 or n=k then 1 elif k>n then 0 else 2*(n-k)*T(n-1, k-1)+2*k*T(n-1, k) fi end: for n from 0 to 9 do [seq(T(n, k), k=0..n)] od; # gives the triangle row by row # Emeric Deutsch, Nov 16 2004

MATHEMATICA

T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, 2*(n-k)*T[n-1, k-1] +2*k*T[n-1, k]]; Table[T[n, k], {n, 0, 9}, {k, 0, n}]//Flatten (* G. C. Greubel, Sep 03 2019 *)

PROG

(PARI) T(n, k) = if(k==0 || k==n, 1, 2*(n-k)*T(n-1, k-1) + 2*k*T(n-1, k));

for(n=0, 9, for(k=0, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Sep 03 2019

(Sage)

def T(n, k):

    if (k==0 or k==n): return 1

    else: return 2*k*T(n-1, k) + 2*(n-k)* T(n-1, k-1)

[[T(n, k) for k in (0..n)] for n in (0..9)] # G. C. Greubel, Sep 03 2019

(GAP)

T:= function(n, k)

    if k=0 or k=n then return 1;

    else return 2*(n-k)*T(n-1, k-1) + 2*k*T(n-1, k);

    fi;

  end;

Flat(List([0..9], n-> List([0..n], k-> T(n, k) ))); # G. C. Greubel, Sep 03 2019

CROSSREFS

Cf. A060187, A099760.

Sequence in context: A080416 A213166 A168619 * A072590 A111636 A220688

Adjacent sequences:  A099756 A099757 A099758 * A099760 A099761 A099762

KEYWORD

easy,tabl,nonn

AUTHOR

Miklos Kristof, Nov 11 2004

EXTENSIONS

More terms from Emeric Deutsch, Nov 16 2004

STATUS

approved

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Last modified April 19 00:18 EDT 2021. Contains 343098 sequences. (Running on oeis4.)