A222035 G.f.: Sum_{n>=0} Product_{k=1..n} (1 - 1/(1 + k*(k+1)*(k+2)/3!*x)).

1, 1, 3, 21, 283, 6501, 234363, 12486181, 939179643, 96206801061, 13036139824123, 2281006244079141, 505073418764455803, 139105885712904768421, 46950396347414793682683, 19169208258193612244036901, 9360235493546553882893232763, 5411227090880585168975672572581

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Example

G.f.: A(x) = 1 + x + 3*x^2 + 21*x^3 + 283*x^4 + 6501*x^5 + 234363*x^6 +...
where, by definition,
A(x) = 1 + 1*x/(1+x) + 1*4*x^2/((1+x)*(1+4*x)) + 1*4*10*x^3/((1+x)*(1+4*x)*(1+10*x)) + 1*4*10*20*x^4/((1+x)*(1+4*x)*(1+10*x)*(1+20*x)) + 1*4*10*20*35*x^5/((1+x)*(1+4*x)*(1+10*x)*(1+20*x)*(1+35*x)) + 1*4*10*20*35*56*x^6/((1+x)*(1+4*x)*(1+10*x)*(1+20*x)*(1+35*x)*(1+56*x)) +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, 1, A=sum(m=0, n, prod(k=1, m, 1-1/(1+k*(k+1)*(k+2)/3!*x +x*O(x^n))))); polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A000292 (tetrahedral numbers)

Sequence in context: A126461 A370741 A000681 * A361214 A171201 A193206

Adjacent sequences: A222032 A222033 A222034 * A222036 A222037 A222038

Keyword

nonn

Author

Paul D. Hanna, Feb 06 2013

Status

approved