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A108084 Triangle, read by rows, where T(0,0) = 1, T(n,k) = 2^n*T(n-1,k) + T(n-1,k-1). 2
1, 2, 1, 8, 6, 1, 64, 56, 14, 1, 1024, 960, 280, 30, 1, 32768, 31744, 9920, 1240, 62, 1, 2097152, 2064384, 666624, 89280, 5208, 126, 1, 268435456, 266338304, 87392256, 12094464, 755904, 21336, 254, 1, 68719476736, 68451041280, 22638755840 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For n > 0, n-th row sum = Product_{i=1..n} (2^i+1) (i.e., A028362(n+1)).

Triangle T(n,k), 0 <= k <= n, read by rows given by [2, 2, 8, 12, 32, 56, 128, 240, 512, ...] DELTA [[1, 0, 2, 0, 4, 0, 8, 0, 16, 0, 32, 0, ...] = A014236(first zero omitted)DELTA A077957 where DELTA is the operator defined in A084938. - Philippe Deléham, Aug 23 2006

LINKS

Table of n, a(n) for n=0..38.

FORMULA

T(n,0) = 2^(n*(n+1)/2) = A006125(n+1). - Philippe Deléham, Nov 05 2006

T(n,k) = 2^binomial(n+1-k,2) * A022166(n,k) for 0 <= k <= n. - Werner Schulte, Mar 25 2019

EXAMPLE

Triangle begins:

      1;

      2,     1;

      8,     6,    1;

     64,    56,   14,    1;

   1024,   960,  280,   30,  1;

  32768, 31744, 9920, 1240, 62, 1;

CROSSREFS

Cf. A028362, A022166, A006125.

Sequence in context: A231846 A039683 A318389 * A108085 A305860 A272983

Adjacent sequences:  A108081 A108082 A108083 * A108085 A108086 A108087

KEYWORD

nonn,tabl

AUTHOR

Gerald McGarvey, Jun 05 2005

STATUS

approved

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Last modified October 1 11:59 EDT 2020. Contains 337443 sequences. (Running on oeis4.)