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A120305 Sum[Sum[(-1)^(i+j)*(i+j)!/(i!j!),{i,0,n}],{j,0,n}]. 1
1, 1, 3, 9, 31, 111, 407, 1513, 5679, 21471, 81643, 311895, 1196131, 4602235, 17757183, 68680169, 266200111, 1033703055, 4020716123, 15662273839, 61092127491, 238582873475, 932758045123, 3650336341239, 14298633670931 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

p divides a((p+1)/2) for prime p=3,11,17,19,41,43,59,67,73,83,89,97,107,113..=A033200[n] Primes congruent to {1, 3} mod 8; or, odd primes of form x^2+2*y^2. p divides a((p-3)/2) for prime p=17,41,73,89,97,113,137..=A007519[n] Primes of form 8n+1.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

a(n) = Sum[Sum[(-1)^(i+j)*(i+j)!/(i!j!),{i,0,n}],{j,0,n}].

Recurrence: 2*n*(3*n-5)*a(n) = 3*(9*n^2 - 19*n + 8)*a(n-1) - 3*(n-1)*(3*n-4)*a(n-2) - 2*(2*n-3)*(3*n-2)*a(n-3). - Vaclav Kotesovec, Aug 13 2013

a(n) ~ 4^(n+1)/(9*sqrt(Pi*n)). - Vaclav Kotesovec, Aug 13 2013

MATHEMATICA

Table[Sum[Sum[(-1)^(i+j)*(i+j)!/(i!j!), {i, 0, n}], {j, 0, n}], {n, 0, 50}]

CROSSREFS

Cf. A033200, A007519.

Sequence in context: A151459 A151033 A047012 * A049170 A049174 A209335

Adjacent sequences:  A120302 A120303 A120304 * A120306 A120307 A120308

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Jul 14 2006

STATUS

approved

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Last modified October 17 22:48 EDT 2018. Contains 316297 sequences. (Running on oeis4.)