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A214724 E.g.f.: exp( Sum_{n>=0} x^(n^2+1)/(n^2+1) ). 0
1, 1, 2, 4, 10, 50, 220, 1240, 6140, 32860, 602200, 5668400, 62030200, 522328600, 4487190800, 62591332000, 715163146000, 30496564010000, 482341877812000, 8342949421288000, 124613700640580000, 1733826182453140000, 36635355834463000000, 597186420007933040000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Conjecture: p | a(n) for n>=p when p is a prime of the form m^2+1 (A002496).

LINKS

Table of n, a(n) for n=0..23.

EXAMPLE

E.g.f.: A(x) = 1 + x + 2*x^2/2! + 4*x^3/3! + 10*x^4/4! + 50*x^5/5! + 220*x^6/6! +...

where, by definition,

log(A(x)) = x + x^2/2 + x^5/5 + x^10/10 + x^17/17 + x^26/26 + x^37/37 +...

PROG

(PARI) {a(n)=n!*polcoeff(exp(sum(k=0, n, x^(k^2+1)/(k^2+1) + x*O(x^n))), n)}

for(n=0, 21, print1(a(n), ", "))

CROSSREFS

Sequence in context: A000613 A322294 A053500 * A326325 A080090 A125263

Adjacent sequences:  A214721 A214722 A214723 * A214725 A214726 A214727

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 26 2012

STATUS

approved

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Last modified February 27 15:39 EST 2020. Contains 332307 sequences. (Running on oeis4.)