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A185412 Triangle T(n,m) read by rows: the matrix product A130595 * A156919. 1
1, 1, 1, 1, 8, 1, 1, 33, 33, 1, 1, 112, 378, 112, 1, 1, 353, 2938, 2938, 353, 1, 1, 1080, 18987, 44912, 18987, 1080, 1, 1, 3265, 111051, 520523, 520523, 111051, 3265, 1, 1, 9824, 612820, 5131040, 9998182, 5131040, 612820, 9824, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Row sums are A165968(n+1).
Because A130595 is the inverse of the Pascal triangle A007318, we have A007318 *(this lower triangular matrix) = A156919.
LINKS
FORMULA
G.f.: 1/(1+x-xy-2x/(1-3xy/(1+x-4x/(1-5xy/(1+x-6x/(1-7xy/(1+x-8x/(1-9xy/(1+ ... (continued fraction).
EXAMPLE
Triangle begins in row n=0 with columns 0 <= m <= n:
1;
1, 1;
1, 8, 1;
1, 33, 33, 1;
1, 112, 378, 112, 1;
1, 353, 2938, 2938, 353, 1;
1, 1080, 18987, 44912, 18987, 1080, 1;
1, 3265, 111051, 520523, 520523, 111051, 3265, 1;
1, 9824, 612820, 5131040, 9998182, 5131040, 612820, 9824, 1;
MAPLE
A156919 := proc(n, m) if n=m then 1; elif m=0 then 2^n ; elif m<0 or m>n then 0; else 2*(m+1)*procname(n-1, m)+(2*n-2*m+1)*procname(n-1, m-1) ; end if; end proc:
A130595 := proc(n, m) (-1)^(n+m)*binomial(n, m) ; end proc:
A185412 := proc(n, m) local a, j; a := 0 ; for j from m to n do a := a+A130595(n, j)*A156919(j, m) ; end do: a ; end proc: # R. J. Mathar, Feb 03 2011
CROSSREFS
Sequence in context: A157208 A178347 A141686 * A157148 A220595 A154335
KEYWORD
nonn,easy,tabl
AUTHOR
Paul Barry, Jan 26 2011
STATUS
approved

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Last modified March 28 07:33 EDT 2024. Contains 371235 sequences. (Running on oeis4.)