A092429 a(n) = n! * Sum_{i,j,k,l >= 0, i+j+k+l = n} 1/(i!*j!*k!*l!).

1, 1, 3, 10, 47, 126, 522, 1821, 8143, 26326, 109958, 396111, 1737122, 5998955, 24949277, 91979985, 397402223, 1418993350, 5881338702, 22010456331, 94022106862, 342803313261, 1416758002487, 5356198979731, 22685035586290, 83911052895151, 345921828889367

Offset

0,3

Comments

a(n) is even iff n is a sum of 2 distinct powers of 2.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Vaclav Kotesovec, Recurrence (of order 11)

Formula

E.g.f.: (t(1)^4 + 6*t(1)^2*t(2) + 8*t(1)*t(3) + 3*t(2)^2 + 6*t(4))/24 where t(1) = hypergeom([],[],x), t(2) = hypergeom([],[1],x^2), t(3) = hypergeom([],[1,1],x^3) and t(4) = hypergeom([],[1,1,1],x^4). - Vladeta Jovovic, Sep 22 2007, typo corrected by Vaclav Kotesovec, Jul 01 2013

Conjecture: a(n) ~ 4^n/4!. - Vaclav Kotesovec, Mar 07 2014

Maple

b:= proc(n, i, t) option remember;
      `if`(t=1, 1/n!, add(b(n-j, j, t-1)/j!, j=i..n/t))
    end:
a:= n-> n!*b(n, 0, 4):
seq(a(n), n=0..30);  # Alois P. Heinz, Sep 21 2017

Mathematica

Table[Sum[Sum[Sum[Sum[If[i+j+k+l==n, n!/i!/j!/k!/l!, 0], {l, 0, k}], {k, 0, j}], {j, 0, i}], {i, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 01 2013 *)
CoefficientList[Series[(HypergeometricPFQ[{}, {}, x]^4 +6*HypergeometricPFQ[{}, {}, x]^2 *HypergeometricPFQ[{}, {1}, x^2] +8*HypergeometricPFQ[{}, {}, x] *HypergeometricPFQ[{}, {1, 1}, x^3] +3*HypergeometricPFQ[{}, {1}, x^2]^2 +6*HypergeometricPFQ[{}, {1, 1, 1}, x^4])/24, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec after Vladeta Jovovic, Jul 01 2013 *)

Prog

(PARI) a(n)=sum(i=0, n, sum(j=0, i, sum(k=0, j, sum(l=0, k, if(i+j+k+l-n, 0, n!/i!/j!/k!/l!)))))

Crossrefs

Cf. A018900, A027306, A092255.

Column k=4 of A226873. - Alois P. Heinz, Jun 21 2013

Sequence in context: A020008 A167999 A000849 * A218919 A346188 A226875

Adjacent sequences: A092426 A092427 A092428 * A092430 A092431 A092432

Keyword

nonn

Author

Benoit Cloitre, Mar 22 2004

Status

approved