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A184359 Recurrence: Sum_{n>=0} a(n-k)*a(k) = (n+1)!^2/2^n. 2
1, 1, 4, 32, 410, 7562, 188736, 6118296, 249991926, 12575954918, 764125698224, 55189878377480, 4674557178309388, 458942541226822876, 51705551381013381112, 6626012145599584408536, 958371653002293850802814 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..16.

FORMULA

Self-convolution equals A184358.

G.f. satisfies: A(x) = F(x*A(x)^2) where A(x/F(x)^2) = F(x) is the g.f. of A184361.

G.f.: A(x) = sqrt((1/x)*Series_Reversion(x/F(x)^2)) where F(x) is the g.f. of A184361.

EXAMPLE

G.f.: A(x) = 1 + x + 4*x^2 + 32*x^3 + 410*x^4 + 7562*x^5 +...

A(x)^2 = 1 + 2*x + 9*x^2 + 72*x^3 + 900*x^4 + 16200*x^5 + 396900*x^6 +...+ (n+1)!^2*x^n/2^n +...

The g.f. of A184361 is F(x) = A(x/F(x)^2):

F(x) = 1 + x + 2*x^2 + 15*x^3 + 204*x^4 + 4085*x^5 + 110128*x^6 +...

PROG

(PARI) {a(n)=local(G=sum(m=0, n, (m+1)!^2*x^m/2^m)+x*O(x^n)); polcoeff(sqrt(G), n)}

CROSSREFS

Cf. A184358, A184360, A184361.

Sequence in context: A243468 A317677 A191459 * A229548 A005172 A298694

Adjacent sequences:  A184356 A184357 A184358 * A184360 A184361 A184362

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 16 2011

STATUS

approved

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Last modified July 29 09:31 EDT 2021. Contains 346344 sequences. (Running on oeis4.)