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A085881 Triangle T(n,k) read by rows: multiply row n of Pascal's triangle (A007318) by A001147(n). 2
1, 1, 1, 3, 6, 3, 15, 45, 45, 15, 105, 420, 630, 420, 105, 945, 4725, 9450, 9450, 4725, 945, 10395, 62370, 155925, 207900, 155925, 62370, 10395, 135135, 945945, 2837835, 4729725, 4729725, 2837835, 945945, 135135, 2027025 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..36.

FORMULA

Triangle given by [1, 2, 3, 4, 5, 6, ...] DELTA [1, 2, 3, 4, 5, 6, ...] where DELTA is Deléham's operator defined in A084938.

T(n,k) = A164961(n,k)/2^n. - Philippe Deléham, Jan 07 2012

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

E.g.f.: 1/sqrt(1-2*x-2*x*y). - Peter Bala, Jul 15 2012

G.f.: W(0), where W(k) = 1 - (k+1)*x*(1+y)/( (k+1)*x*(1+y) - 1/W(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Nov 03 2013

EXAMPLE

Triangle starts

1,

1, 1,

3, 6, 3,

15, 45, 45, 15,

105, 420, 630, 420, 105,

945, 4725, 9450, 9450, 4725, 945,

...

CROSSREFS

Cf. A084938, A164961

Sequence in context: A109044 A205844 A205865 * A127574 A169842 A185588

Adjacent sequences:  A085878 A085879 A085880 * A085882 A085883 A085884

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Aug 17 2003

STATUS

approved

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Last modified April 20 13:33 EDT 2014. Contains 240806 sequences.