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A173503 Triangle T(n, k, q) = c(n, q)/(c(k, q)*c(n-k, q)) where c(n,q) = Product_{j=1..n} (q^j -1)^(n-j) and q = 2, read by rows. 2
1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 21, 63, 21, 1, 1, 315, 6615, 6615, 315, 1, 1, 9765, 3075975, 21531825, 3075975, 9765, 1, 1, 615195, 6007379175, 630774813375, 630774813375, 6007379175, 615195, 1, 1, 78129765, 48065040779175, 156451707736214625, 2346775616043219375, 156451707736214625, 48065040779175, 78129765, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

G. C. Greubel, Rows n = 0..29 of the triangle, flattened

FORMULA

T(n, k, q) = c(n, q)/(c(k, q)*c(n-k, q)) where c(n,q) = Product_{j=1..n} (q^j -1)^(n-j) and q = 2.

EXAMPLE

The triangle begins as:

  1;

  1,      1;

  1,      1,          1;

  1,      3,          3,            1;

  1,     21,         63,           21,            1;

  1,    315,       6615,         6615,          315,          1;

  1,   9765,    3075975,     21531825,      3075975,       9765,      1;

  1, 615195, 6007379175, 630774813375, 630774813375, 6007379175, 615195, 1;

MATHEMATICA

c[n_, q_]:= Product[(q^m-1)^(n-m), {m, 1, n}];

T[n_, k_, q_]:= c[n, q]/(c[k, q]*c[n-k, q]);

Table[T[n, k, 2], {n, 0, 10}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Apr 25 2021 *)

PROG

(Sage)

@CachedFunction

def c(n, q): return product( (q^j -1)^(n-j) for j in (1..n))

def T(n, k, q): return c(n, q)/(c(k, q)*c(n-k, q))

flatten([[T(n, k, 2) for k in (0..n)] for n in (0..10)]) # G. C. Greubel, Apr 25 2021

CROSSREFS

Cf. A173504, A173505.

Sequence in context: A087107 A155170 A126460 * A338114 A100940 A344390

Adjacent sequences:  A173500 A173501 A173502 * A173504 A173505 A173506

KEYWORD

nonn,tabl,less

AUTHOR

Roger L. Bagula, Feb 20 2010

EXTENSIONS

Edited by G. C. Greubel, Apr 25 2021

STATUS

approved

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Last modified October 24 20:35 EDT 2021. Contains 348233 sequences. (Running on oeis4.)