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A105060
Triangle read by rows in which the n-th row consists of the first n nonzero terms of A033312.
2
1, 1, 5, 1, 5, 23, 1, 5, 23, 119, 1, 5, 23, 119, 719, 1, 5, 23, 119, 719, 5039, 1, 5, 23, 119, 719, 5039, 40319, 1, 5, 23, 119, 719, 5039, 40319, 362879, 1, 5, 23, 119, 719, 5039, 40319, 362879, 3628799, 1, 5, 23, 119, 719, 5039, 40319, 362879, 3628799, 39916799
OFFSET
1,3
FORMULA
From G. C. Greubel, Mar 13 2023: (Start)
T(n, k) = T(n,k-1) + k*k!, with T(n, 1) = 1.
Sum_{k=1..n} T(n, k) = -A007489(n+2) + (n+4)*A007489(n+1) - (n+2)*A007489(n) - (n+1). (End)
EXAMPLE
Triangle begins as:
1;
1, 5;
1, 5, 23;
1, 5, 23, 119;
1, 5, 23, 119, 719;
1, 5, 23, 119, 719, 5039;
1, 5, 23, 119, 719, 5039, 40319;
MATHEMATICA
a[n_]:= a[n]= If[n==1, 1, a[n-1] + k!*n];
Table[a[k], {n, 12}, {k, n}]//Flatten
PROG
(Magma)
function T(n, k)
if k eq 1 then return 1;
else return T(n, k-1) + k*Factorial(k);
end if;
end function;
[T(n, k): k in [1..n], n in [1..12]]; // G. C. Greubel, Mar 13 2023
(SageMath)
@CachedFunction
def T(n, k):
if (k==1): return 1
else: return T(n, k-1) + k*factorial(k)
flatten([[T(n, k) for k in range(1, n+1)] for n in range(1, 10)]) # G. C. Greubel, Mar 13 2023
CROSSREFS
Sequence in context: A101692 A281105 A327283 * A229096 A290797 A375066
KEYWORD
nonn,easy,tabl
AUTHOR
Roger L. Bagula, Apr 05 2005
STATUS
approved