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A224608 G.f.: exp( Sum_{n>=1} A219331(n^2)*x^n/n ). 3
1, 1, 3, 12, 81, 1335, 49309, 3882180, 633703214, 212061201327, 144669917959584, 200541263416077021, 563631413420071614333, 3206926569346230863485855, 36897315109526505791310840932, 857701705296285206387609947414980, 40254707002970300021370965171570478599 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A219331 is the logarithmic derivative of A006456, where A006456(n) is the number of compositions of n into sums of squares.

LINKS

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

FORMULA

Logarithmic derivative yields A224607, where A224607(n) = A219331(n^2).

EXAMPLE

G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 81*x^4 + 1335*x^5 + 49309*x^6 +...

where

log(A(x)) = x + 5*x^2/2 + 28*x^3/3 + 269*x^4/4 + 6181*x^5/5 + 286790*x^6/6 +...+ A219331(n^2)*x^n/n +...

PROG

(PARI) {A219331(n)=n*polcoeff(-log(1-sum(r=1, sqrtint(n+1), x^(r^2)+x*O(x^n))), n)}

{a(n)=polcoeff(exp(sum(m=1, n, A219331(m^2)*x^m/m)+x*O(x^n)), n)}

for(n=0, 20, print1(a(n), ", "))

CROSSREFS

Cf. A224607, A219331, A006456, A224366.

Sequence in context: A303033 A207322 A188227 * A023881 A067111 A171186

Adjacent sequences:  A224605 A224606 A224607 * A224609 A224610 A224611

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Apr 12 2013

STATUS

approved

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Last modified December 2 00:55 EST 2021. Contains 349435 sequences. (Running on oeis4.)