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A156367 Number triangle T(n,k)=C(n+k,2k)*k! 2
1, 1, 1, 1, 3, 2, 1, 6, 10, 6, 1, 10, 30, 42, 24, 1, 15, 70, 168, 216, 120, 1, 21, 140, 504, 1080, 1320, 720, 1, 28, 252, 1260, 3960, 7920, 9360, 5040, 1, 36, 420, 2772, 11880, 34320, 65520, 75600, 40320, 1, 45, 660, 5544, 30888, 120120, 327600, 604800 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are A155857. Diagonal sums are A084261. Reversal of A155856.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: 1/(1-x-xy/(1-x-xy/(1-x-2xy/(1-x-2xy/(1-x-3xy/(1-x-3xy/(1-... (continued fraction).

EXAMPLE

Triangle begins

1,

1, 1,

1, 3, 2,

1, 6, 10, 6,

1, 10, 30, 42, 24,

1, 15, 70, 168, 216, 120,

1, 21, 140, 504, 1080, 1320, 720,

1, 28, 252, 1260, 3960, 7920, 9360, 5040,

1, 36, 420, 2772, 11880, 34320, 65520, 75600, 40320

MATHEMATICA

Flatten[Table[Binomial[n+k, 2k]k!, {n, 0, 10}, {k, 0, n}]] (* Harvey P. Dale, Jun 17 2015 *)

CROSSREFS

Sequence in context: A088617 A190909 A144250 * A193593 A181853 A008276

Adjacent sequences:  A156364 A156365 A156366 * A156368 A156369 A156370

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Feb 08 2009

STATUS

approved

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Last modified October 24 01:08 EDT 2018. Contains 316541 sequences. (Running on oeis4.)