A164961 Triangle read by rows: T[n,m] = quadruple factorials A001813(n) * binomials A007318(n,m).

1, 2, 2, 12, 24, 12, 120, 360, 360, 120, 1680, 6720, 10080, 6720, 1680, 30240, 151200, 302400, 302400, 151200, 30240, 665280, 3991680, 9979200, 13305600, 9979200, 3991680, 665280, 17297280, 121080960, 363242880, 605404800, 605404800

Offset

0,2

Comments

Row sums give A052714. - Tilman Neumann, Sep 07 2009

Triangle T(n,k), read by rows, given by (2, 4, 6, 8, 10, 12, 14, ...) DELTA (2, 4, 6, 8, 10, 12, 14, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Jan 07 2012

Links

Table of n, a(n) for n=0..32.

More terms. - Tilman Neumann, Sep 07 2009

Formula

T(n,k) = A085881(n,k)*2^n. - Philippe Deléham, Jan 07 2012

Recurrence equation: T(n+1,k) = (4*n+2)*(T(n,k) + T(n,k-1)). - Peter Bala, Jul 15 2012

E.g.f.: 1/sqrt(1-4*x-4*x*y). - Peter Bala, Jul 15 2012

Example

Triangle begins:
  1
  2, 2
  12, 24, 12
  120, 360, 360, 120
  1680, 6720, 10080, 6720, 1680

Crossrefs

Cf. A001813, A007318, A052714 (row sums), A084938, A085881.

Sequence in context: A303537 A369086 A355871 * A362192 A122007 A365643

Adjacent sequences: A164958 A164959 A164960 * A164962 A164963 A164964

Keyword

nonn,tabl

Author

Tilman Neumann, Sep 02 2009

Status

approved