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A168422 Number triangle with row sums given by quadruple factorial numbers A001813. 0
1, 1, 1, 7, 4, 1, 71, 39, 9, 1, 1001, 536, 126, 16, 1, 18089, 9545, 2270, 310, 25, 1, 398959, 208524, 49995, 7120, 645, 36, 1, 0, 10391023, 5394991, 1301139, 190435, 18445, 1197, 49, 1, 312129649, 161260336, 39066076, 5828704, 589750, 41776, 2044 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Reversal of coefficient array for the polynomials P(n,x)=sum{k=0..n, (C(n+k,2k)(2k)!/k!)*x^k*(1-x)^(n-k)}.

Note that P(n,x)=sum{k=0..n, A113025(n,k)*x^k*(1-x)^(n-k)}. Row sums are A001813.

LINKS

Table of n, a(n) for n=0..43.

FORMULA

Number triangle T(n,k)=T(n,k)=(1/k!)*sum{j=0..n, (-1)^(j-k)*(2n-j)!/((n-j)!*(j-k)!)}

EXAMPLE

Triangle begins

1,

1, 1,

7, 4, 1,

71, 39, 9, 1,

1001, 536, 126, 16, 1,

18089, 9545, 2270, 310, 25, 1,

398959, 208524, 49995, 7120, 645, 36, 1,

10391023, 5394991, 1301139, 190435, 18445, 1197, 49, 1,

312129649, 161260336, 39066076, 5828704, 589750, 41776, 2044, 64, 1

Production matrix begins

1, 1,

6, 3, 1,

40, 20, 5, 1,

336, 168, 42, 7, 1,

3456, 1728, 432, 72, 9, 1,

42240, 21120, 5280, 880, 110, 11, 1,

599040, 299520, 74880, 12480, 1560, 156, 13, 1,

9676800, 4838400, 1209600, 201600, 25200, 2520, 210, 15, 1

Complete this with a top row (1,0,0,0,...) and invert: we get

1,

-1, 1,

-3, -3, 1,

-5, -5, -5, 1,

-7, -7, -7, -7, 1,

-9, -9, -9, -9, -9, 1,

-11, -11, -11, -11, -11, -11, 1,

-13, -13, -13, -13, -13, -13, -13, 1,

-15, -15, -15, -15, -15, -15, -15, -15, 1,

-17, -17, -17, -17, -17, -17, -17, -17, -17, 1

CROSSREFS

Cf. A079267.

Sequence in context: A258330 A011407 A021907 * A187056 A103240 A155531

Adjacent sequences:  A168419 A168420 A168421 * A168423 A168424 A168425

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Nov 25 2009

STATUS

approved

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Last modified August 13 05:41 EDT 2020. Contains 336442 sequences. (Running on oeis4.)