A064095 Row sums of triangle A064094.

1, 2, 3, 5, 11, 34, 142, 753, 4826, 36028, 305133, 2879841, 29909422, 338479430, 4139716659, 54339861531, 761150445735, 11322139144240, 178116143657890, 2952831190016239, 51423702126549167, 938126972940647198, 17883424301972473340, 355435808475002747565, 7350551776003412371185

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..475

Mathematica

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) ];
A064095[n_]:= Sum[A064094[n, k], {k, 0, n}];
Table[A064095[n], {n, 0, 30}] (* G. C. Greubel, Sep 27 2024 *)

Prog

(PARI)
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
a(n) = sum(k=0, n, T(n, k));
(Magma)
function A064094(n, k)
  if k eq 0 or k eq n then return 1;
  else return (&+[(n-k-j)*Binomial(n-k-1+j, j)*k^j: j in [0..n-k-1]])/(n-k);
  end if;
end function;
A064095:= func< n | (&+[A064094(n, k): k in [0..n]]) >;
[A064095(n): n in [0..30]]; // G. C. Greubel, Sep 27 2024
(SageMath)
def A064094(n, k):
    if (k==0 or k==n): return 1
    else: return sum((n-k-j)*binomial(n-k-1+j, j)*k^j for j in range(n-k))//(n-k)
def A064095(n): return sum(A064094(n, k) for k in range(n+1))
[A064095(n) for n in range(31)] # G. C. Greubel, Sep 27 2024

Crossrefs

Cf. A064094.

Sequence in context: A124538 A124627 A305971 * A061935 A067078 A124561

Adjacent sequences: A064092 A064093 A064094 * A064096 A064097 A064098

Keyword

nonn,easy

Author

Wolfdieter Lang, Sep 13 2001

Extensions

More terms from Michel Marcus, Oct 28 2022

Status

approved