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A090683 Triangle read by rows, defined by T(n,k)=C(n,k)*S2(n,k), 0<=k<=n, where C(n,k) are the binomial coefficients and S2(n,k) are the Stirling numbers of the second kind. 1
1, 0, 1, 0, 2, 1, 0, 3, 9, 1, 0, 4, 42, 24, 1, 0, 5, 150, 250, 50, 1, 0, 6, 465, 1800, 975, 90, 1, 0, 7, 1323, 10535, 12250, 2940, 147, 1, 0, 8, 3556, 54096, 119070, 58800, 7448, 224, 1, 0, 9, 9180, 254100, 979020, 875826, 222264, 16632, 324, 1, 0, 10, 22995, 1119600, 7162050, 10716300, 4793670, 705600, 33750, 450, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

T(n, k) = A007318(n, k)*A048993(n, k).

T(n, k) = A090657(n, k)/k!.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..230

FORMULA

T(n, k) = binomial(n,k)*stirling2(n,k).

EXAMPLE

Table begins:

{1};

{0, 1};

{0, 2, 1 };

{0, 3, 9, 1};

{0, 4, 42, 24, 1};

...

MATHEMATICA

Flatten[Table[Table[Binomial[n, k] StirlingS2[n, k], {k, 0, n}], {n, 0, 10}], 1]

PROG

(Maxima) create_list(binomial(n, k)*stirling2(n, k), n, 0, 12, k, 0, n); /* Emanuele Munarini, Mar 11 2011 */

CROSSREFS

Cf. A007318, A048993, A090657.

Row sum sequence is A122455.

Sequence in context: A263426 A278882 A153007 * A320825 A161552 A095859

Adjacent sequences:  A090680 A090681 A090682 * A090684 A090685 A090686

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Dec 18 2003

EXTENSIONS

Edited by Olivier Gérard, Oct 23 2012

STATUS

approved

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Last modified October 16 03:34 EDT 2019. Contains 328040 sequences. (Running on oeis4.)