login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A132875 Triangle T, read by rows, where g.f. of row n of T^n = (y + n*(n+1))^n for n>=0 and T^n denotes the n-th matrix power of T. 6
1, 2, 1, 12, 6, 1, 240, 72, 12, 1, 12400, 2240, 240, 20, 1, 1242720, 157200, 10800, 600, 30, 1, 202721064, 20017032, 1000440, 36960, 1260, 42, 1, 48537596352, 3986643136, 159475008, 4390400, 101920, 2352, 56, 1, 15957585674496, 1133413590528 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Pascal's triangle, B, obeys: the g.f. of row n of B^n = (y + n)^n for n>=0; this triangle has a similar property.

LINKS

Table of n, a(n) for n=0..37.

FORMULA

C(n,k) divides T(n,k) for n>=k>=0.

EXAMPLE

Triangle begins:

1;

2, 1;

12, 6, 1;

240, 72, 12, 1;

12400, 2240, 240, 20, 1;

1242720, 157200, 10800, 600, 30, 1;

202721064, 20017032, 1000440, 36960, 1260, 42, 1;

48537596352, 3986643136, 159475008, 4390400, 101920, 2352, 56, 1;

15957585674496, 1133413590528, 38423427840, 860840064, 15140160, 241920, 4032, 72, 1; ...

Matrix square T^2 begins:

1;

4, 1;

36, 12, 1; <== g.f. of row 2: (y + 2*3)^2

768, 216, 24, 1;

36960, 7360, 720, 40, 1;

3445440, 489600, 36000, 1800, 60, 1; ...

Matrix cube T^3 begins:

1;

6, 1;

72, 18, 1;

1728, 432, 36, 1; <== g.f. of row 3: (y + 3*4)^3

82320, 16800, 1440, 60, 1;

7275360, 1126800, 82800, 3600, 90, 1; ...

Matrix 4th power T^4 begins:

1;

8, 1;

120, 24, 1;

3264, 720, 48, 1;

160000, 32000, 2400, 80, 1; <== g.f. of row 4: (y + 4*5)^4

13745280, 2241600, 158400, 6000, 120, 1; ...

PROG

(PARI) {T(n, k)=local(M=Mat(1), N, L); for(i=1, n, N=M; M=matrix(#N+1, #N+1, r, c, if(r>=c, if(r<=#N, (N^(#N))[r, c], polcoeff((x+(#M)*(#M+1))^(#M), c-1)))); L=sum(i=1, #M, -(M^0-M)^i/i); M=sum(i=0, #M, (L/#N)^i/i!); ); M[n+1, k+1]}

CROSSREFS

Cf. A132876 (row sums); columns: A132877, A132878; A132879; variant: A132870.

Sequence in context: A008285 A119274 A066991 * A050139 A010255 A257635

Adjacent sequences:  A132872 A132873 A132874 * A132876 A132877 A132878

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Sep 29 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 17 03:06 EST 2019. Contains 329216 sequences. (Running on oeis4.)