A198891 -id:A198891 - cp's OEIS frontend

A205802 Expansion of e.g.f. 1/( Sum_{n>=0} (-x)^(n^2) / (n^2)! ).

1, 1, 2, 6, 23, 110, 630, 4200, 31990, 274051, 2608220, 27304530, 311820630, 3857738170, 51397726380, 733698365400, 11171708347799, 180738402744866, 3096027531044102, 55980949167688884, 1065496642477438890, 21293801805033731190, 445818117237227995260

Offset: 0

Paul D. Hanna, Jan 31 2012

nonn

			E.g.f.: A(x) = 1 + x + 2*x^2/2! + 6*x^3/3! + 23*x^4/4! + 110*x^5/5! + ...
where
1/A(x) = 1 - x + x^4/4! - x^9/9! + x^16/16! - x^25/25! + x^36/36! + ...

Paul D. Hanna, Table of n, a(n) for n = 0..400

Cf. A198891, A205800, A205801.

{a(n)=n!*polcoeff(sum(m=0, sqrtint(n+1), (-1)^m*x^(m^2)/(m^2)!+x*O(x^n))^(-1), n)}
for(n=0,25,print1(a(n),", "))

E.g.f.: 1/( Sum_{n>=0} (-x)^(n^2) / (n^2)! ).

A198892 E.g.f.: 1/[ Sum_{n>=0} (-x)^(n*(n+1)/2) / A000178(n) ] where A000178(n) = Product_{k=1..n} k!.

Original entry on oeis.org

1, 1, 2, 9, 48, 300, 2280, 20580, 211680, 2434320, 31134600, 438807600, 6744276000, 112237725600, 2011760150400, 38639999197800, 791610365145600, 17230493212732800, 397111119429024000, 9660782144094681600, 247393077222459168000, 6651976858409613931200

Offset: 0

Paul D. Hanna, Oct 30 2011

nonn

			E.g.f.: A(x) = 1 + x + 2*x^2/2! + 9*x^3/3! + 48*x^4/4! + 300*x^5/5! +...
where
1/A(x) = 1 - x/1! - x^3/(1!*2!) + x^6/(1!*2!*3!) + x^10/(1!*2!*3!*4!) - x^15/(1!*2!*3!*4!*5!) - x^21/(1!*2!*3!*4!*5!*6!) ++--...
1/A(x) = 1 - x - x^3/2 + x^6/12 + x^10/288 - x^15/34560 - x^21/24883200 +...

Cf. A198891.

{a(n) = my(A=1/sum(m=0,sqrtint(2*n+1), (-x)^(m*(m+1)/2) / prod(k=1,m,k!)+x*O(x^n))); n!*polcoeff(A,n)}
for(n=0,25,print1(a(n),", "))

cp's OEIS Frontend

A205802 Expansion of e.g.f. 1/( Sum_{n>=0} (-x)^(n^2) / (n^2)! ).

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