cp's OEIS Frontend

A080955 Square array of numbers related to the incomplete gamma function, read by antidiagonals.

%I A080955 #16 Mar 08 2018 13:18:53
%S A080955 1,1,1,1,2,2,1,3,5,6,1,4,10,16,24,1,5,17,38,65,120,1,6,26,78,168,326,
%T A080955 720,1,7,37,142,393,872,1957,5040,1,8,50,236,824,2208,5296,13700,
%U A080955 40320,1,9,65,366,1569,5144,13977,37200,109601,362880,1,10,82,538,2760,10970,34960,100026
%N A080955 Square array of numbers related to the incomplete gamma function, read by antidiagonals.
%F A080955 T(k,n) = n! * Sum{j=0..n} k^j/j!.
%F A080955 E.g.f. of k-th row: exp(k*x)/(1-x).
%F A080955 T(k,n) = A089258(n,k).
%e A080955 Array begins:
%e A080955 k=0: 1 1 2 6 24 ...
%e A080955 k=1: 1 2 5 16 65 ...
%e A080955 k=2: 1 3 10 38 168 ...
%e A080955 k=3: 1 4 17 78 393 ...
%e A080955 k=4: 1 5 26 142 824 ...
%e A080955 ...
%t A080955 T[0, k_] := k!; T[n_, k_] := k!*Sum[n^j/j!, {j, 0, k}];
%t A080955 Table[T[n-k, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Jan 17 2018 *)
%Y A080955 Rows: A000142, A000522, A010842, A053486, A053487, A080954.
%Y A080955 Transposed version: A089258.
%K A080955 easy,nonn,tabl
%O A080955 0,5
%A A080955 _Paul Barry_, Feb 26 2003
%E A080955 Corrected by _Philippe Deléham_, Dec 12 2003