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A193438 E.g.f.: exp( Sum_{n>=0} x^(4*n+1)/(4*n+1) ). 1
1, 1, 1, 1, 1, 25, 145, 505, 1345, 43345, 481825, 3027025, 13679425, 528618025, 8796735025, 81517983625, 529655946625, 23619691278625, 526089195906625, 6512769913326625, 55783484692170625, 2802281186570685625, 78369733286598300625, 1221751619270220585625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Conjecture: a(n) is divisible by 5^floor(n/5) for n>=0.

Conjecture: a(n) is divisible by p^floor(n/p) for prime p == 1 (mod 4).

LINKS

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

EXAMPLE

E.g.f.: A(x) = 1 + x + x^2/2! + x^3/3! + x^4/4! + 25*x^5/5! + 145*x^6/6! + 505*x^7/7! +...

where

log(A(x)) = x + x^5/5 + x^9/9 + x^13/13 + x^17/17 + x^21/21 + x^25/25 +...

PROG

(PARI) {a(n)=n!*polcoeff( exp(sum(m=0, n, x^(4*m+1)/(4*m+1))+x*O(x^n)) , n)}

CROSSREFS

Cf. A193437.

Sequence in context: A100255 A305269 A052501 * A139152 A123014 A095971

Adjacent sequences:  A193435 A193436 A193437 * A193439 A193440 A193441

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 25 2011

STATUS

approved

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Last modified October 20 12:34 EDT 2018. Contains 316379 sequences. (Running on oeis4.)