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A146990 Triangle, read by rows, T(n, k) = binomial(n, k) for n < 2 and binomial(n, k) + n^(n-1) * binomial(n-2, k-1) otherwise.

%I A146990 #10 Feb 06 2025 07:38:19
%S A146990 1,1,1,1,4,1,1,12,12,1,1,68,134,68,1,1,630,1885,1885,630,1,1,7782,
%T A146990 31119,46676,31119,7782,1,1,117656,588266,1176525,1176525,588266,
%U A146990 117656,1,1,2097160,12582940,31457336,41943110,31457336,12582940,2097160,1
%N A146990 Triangle, read by rows, T(n, k) = binomial(n, k) for n < 2 and binomial(n, k) + n^(n-1) * binomial(n-2, k-1) otherwise.
%C A146990 Row sums are: {1, 2, 6, 26, 272, 5032, 124480, 3764896, 134217984, 5509980800, 256000001024, ...}.
%H A146990 G. C. Greubel, <a href="/A146990/b146990.txt">Rows n = 0..100 of triangle, flattened</a>
%F A146990 T(n, k) = binomial(n, k) for n < 2 and binomial(n, k) + n^(n-1) * binomial(n-2, k-1) otherwise.
%e A146990 Triangle begins as:
%e A146990   1;
%e A146990   1,    1;
%e A146990   1,    4,     1;
%e A146990   1,   12,    12,     1;
%e A146990   1,   68,   134,    68,     1;
%e A146990   1,  630,  1885,  1885,   630,    1;
%e A146990   1, 7782, 31119, 46676, 31119, 7782, 1;
%p A146990 seq(seq( `if`(n<2, binomial(n,k), binomial(n,k) + n^(n-1)*binomial(n-2,k-1)), k=0..n), n=0..10); # _G. C. Greubel_, Jan 09 2020
%t A146990 Table[If[n <2, Binomial[n, m], Binomial[n, m] + n^(n - 1)*Binomial[n - 2, m - 1]], {n, 0, 10}, {m, 0, n}]; Flatten[%]
%o A146990 (PARI) T(n,k) = if(n<2, binomial(n,k), binomial(n,k) + n^(n-1)*binomial(n-2,k-1) ); \\ _G. C. Greubel_, Jan 09 2020
%o A146990 (Magma) T:= func< n,k | n lt 2 select Binomial(n,k) else Binomial(n,k) + n^(n-1)*Binomial(n-2,k-1) >;
%o A146990 [T(n,k): k in [0..n], n in [0..10]]; // _G. C. Greubel_, Jan 09 2020
%o A146990 (Sage)
%o A146990 @CachedFunction
%o A146990 def T(n, k):
%o A146990     if (n<2): return binomial(n,k)
%o A146990     else: return binomial(n,k) + n^(n-1)*binomial(n-2,k-1)
%o A146990 [[T(n, k) for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, Jan 09 2020
%o A146990 (GAP)
%o A146990 T:= function(n,k)
%o A146990     if n<2 then return Binomial(n,k);
%o A146990     else return Binomial(n,k) + n^(n-1)*Binomial(n-2,k-1);
%o A146990     fi; end;
%o A146990 Flat(List([0..10], n-> List([0..n], k-> T(n,k) ))); # _G. C. Greubel_, Jan 09 2020
%Y A146990 Cf. A028262.
%K A146990 nonn,tabl
%O A146990 0,5
%A A146990 _Roger L. Bagula_, Nov 04 2008
%E A146990 Edited by _G. C. Greubel_, Jan 09 2020