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A218685 O.g.f.: Sum_{n>=0} (1+n^3*x)^n * x^n/n! * exp(-(1+n^3*x)*x). 3
1, 0, 1, 6, 34, 270, 3415, 31230, 681026, 6949920, 230637870, 2546120514, 119281951006, 1394371349490, 87612425583018, 1069010047029672, 86763885548985810, 1094149501538197236, 111443560982774811439, 1442387644419293694144, 180179254059921915232864 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
Compare the o.g.f. to the curious identity:
1/(1-x^2) = Sum_{n>=0} (1+n*x)^n * x^n/n! * exp(-(1+n*x)*x).
LINKS
EXAMPLE
O.g.f: A(x) = 1 + x^2 + 6*x^3 + 34*x^4 + 270*x^5 + 3415*x^6 +...
where
A(x) = exp(-x) + (1+x)*x*exp(-(1+x)*x) + (1+2^3*x)^2*x^2/2!*exp(-(1+2^3*x)*x) + (1+3^3*x)^3*x^3/3!*exp(-(1+3^3*x)*x) + (1+4^3*x)^4*x^4/4!*exp(-(1+4^3*x)*x) + (1+5^3*x)^5*x^5/5!*exp(-(1+5^3*x)*x) +...
simplifies to a power series in x with integer coefficients.
PROG
(PARI) {a(n)=polcoeff(sum(k=0, n, (1+k^3*x)^k*x^k/k!*exp(-x*(1+k^3*x)+x*O(x^n))), n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
Sequence in context: A197436 A334787 A302148 * A108432 A355887 A337350
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 05 2012
STATUS
approved

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Last modified July 13 18:16 EDT 2024. Contains 374285 sequences. (Running on oeis4.)