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A156991 Triangle T(n,k) read by rows: T(n,k) = n! * binomial(n + k - 1, n). 2
1, 0, 1, 0, 2, 6, 0, 6, 24, 60, 0, 24, 120, 360, 840, 0, 120, 720, 2520, 6720, 15120, 0, 720, 5040, 20160, 60480, 151200, 332640, 0, 5040, 40320, 181440, 604800, 1663200, 3991680, 8648640, 0, 40320, 362880, 1814400, 6652800, 19958400, 51891840, 121080960, 259459200 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums give A092956(n-1) for n > 0.

Apart from the left column of (essentially) zeros, the same as A105725. - R. J. Mathar, Mar 02 2009

REFERENCES

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 98

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

EXAMPLE

Triangle begins as:

  1;

  0,     1;

  0,     2,      6;

  0,     6,     24,      60;

  0,    24,    120,     360,     840;

  0,   120,    720,    2520,    6720,    15120;

  0,   720,   5040,   20160,   60480,   151200,   332640;

  0,  5040,  40320,  181440,  604800,  1663200,  3991680,   8648640;

  0, 40320, 362880, 1814400, 6652800, 19958400, 51891840, 121080960, 259459200;

  ...

MATHEMATICA

Table[n!*Binomial[n+k-1, n], {n, 0, 12}, {k, 0, n}]//Flatten

PROG

(PARI) for(n=0, 10, for(k=0, n, print1(n!*binomial(n+k-1, n), ", "))) \\ G. C. Greubel, Nov 19 2017

(Sage) flatten([[factorial(n)*binomial(n+k-1, n) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, May 10 2021

CROSSREFS

Cf. A092956, A105725.

Sequence in context: A350256 A345208 A241810 * A229586 A294789 A197035

Adjacent sequences:  A156988 A156989 A156990 * A156992 A156993 A156994

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula, Feb 20 2009

STATUS

approved

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Last modified January 26 06:37 EST 2022. Contains 350572 sequences. (Running on oeis4.)