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A222035
G.f.: Sum_{n>=0} Product_{k=1..n} (1 - 1/(1 + k*(k+1)*(k+2)/3!*x)).
0
1, 1, 3, 21, 283, 6501, 234363, 12486181, 939179643, 96206801061, 13036139824123, 2281006244079141, 505073418764455803, 139105885712904768421, 46950396347414793682683, 19169208258193612244036901, 9360235493546553882893232763, 5411227090880585168975672572581
OFFSET
0,3
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 06 2013
STATUS
approved