A064095 - OEIS

%I #10 Sep 27 2024 07:49:16

%S 1,2,3,5,11,34,142,753,4826,36028,305133,2879841,29909422,338479430,

%T 4139716659,54339861531,761150445735,11322139144240,178116143657890,

%U 2952831190016239,51423702126549167,938126972940647198,17883424301972473340,355435808475002747565,7350551776003412371185

%N Row sums of triangle A064094.

%H G. C. Greubel, <a href="/A064095/b064095.txt">Table of n, a(n) for n = 0..475</a>

%t A064094[n_, k_]:= If[k==0 || k==n, 1, Sum[(n-k-j)*Binomial[n-k-1+j, j]*k^j, {j,0,n-k-1}]/(n-k) ];

%t A064095[n_]:= Sum[A064094[n,k], {k,0,n}];

%t Table[A064095[n], {n,0,30}] (* _G. C. Greubel_, Sep 27 2024 *)

%o (PARI)

%o T(n, k)= if (n==k, 1, sum(i=0, n-k-1, (n-k-i)*binomial(n-k-1+i, i)*(k^i)/(n-k))); \\ A064094

%o a(n) = sum(k=0, n, T(n,k));

%o (Magma)

%o function A064094(n,k)

%o   if k eq 0 or k eq n then return 1;

%o   else return (&+[(n-k-j)*Binomial(n-k-1+j, j)*k^j: j in [0..n-k-1]])/(n-k);

%o   end if;

%o end function;

%o A064095:= func< n | (&+[A064094(n,k): k in [0..n]]) >;

%o [A064095(n): n in [0..30]]; // _G. C. Greubel_, Sep 27 2024

%o (SageMath)

%o def A064094(n,k):

%o     if (k==0 or k==n): return 1

%o     else: return sum((n-k-j)*binomial(n-k-1+j, j)*k^j for j in range(n-k))//(n-k)

%o def A064095(n): return sum(A064094(n,k) for k in range(n+1))

%o [A064095(n) for n in range(31)] # _G. C. Greubel_, Sep 27 2024

%Y Cf. A064094.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Sep 13 2001

%E More terms from _Michel Marcus_, Oct 28 2022