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A347429 a(n) is the alternating sum of the n-th row of A047920. 2

%I #15 Jun 04 2022 04:34:25

%S 1,1,2,3,18,47,516,1851,28502,128943,2546352,13889291,334552866,

%T 2135390367,60692391308,443650121787,14531752130766,119684543973551,

%U 4438679955367752,40666524402277323,1684291581885909722,16989963249272202591,777243725319000331236

%N a(n) is the alternating sum of the n-th row of A047920.

%H Alois P. Heinz, <a href="/A347429/b347429.txt">Table of n, a(n) for n = 0..450</a>

%F a(n) = Sum_{k=0..n} (-1)^k * A047920(n,k).

%p b:= proc(n, k) option remember;

%p `if`(k=0, n!, b(n, k-1)-b(n-1, k-1))

%p end:

%p a:= n-> add(b(n, k)*(-1)^k, k=0..n):

%p seq(a(n), n=0..23);

%t a[n_] := Sum[(-1)^(j+k)*Binomial[k, j]*(n-j)!, {j, 0, n}, {k, 0, n}];

%t Table[a[n], {n, 0, 23}] (* _Jean-Fran├žois Alcover_, Jun 04 2022 *)

%o (PARI) row(n) = vector(n+1, k, k--; sum(j=0, n, (-1)^j * binomial(k, j)*(n-j)!)); \\ A047920

%o a(n) = my(v=row(n)); sum(k=1, n+1, (-1)^k*row[k]); \\ _Michel Marcus_, Sep 04 2021

%Y Cf. A047920.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Sep 01 2021

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Last modified April 18 08:27 EDT 2024. Contains 371769 sequences. (Running on oeis4.)