A198891 - OEIS

A198891

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

1, 1, 2, 7, 32, 180, 1219, 9646, 87192, 886536, 10016159, 124481258, 1687686528, 24787991800, 392081193504, 6644677619581, 120115898158288, 2307044712629472, 46917527736860976, 1007152702625923440, 22757886107313170356, 539955309450787483261, 13421068671117864869156

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..22.

EXAMPLE

E.g.f.: A(x) = 1 + x + 2*x^2/2! + 7*x^3/3! + 32*x^4/4! + 180*x^5/5! + ... + a(n)*x^n/n! + ...

where

1/A(x) = 1 - x - x^3/3! + x^6/6! + x^10/10! - x^15/15! - x^21/21! ++-- ... + (-x)^(n*(n+1)/2)/(n*(n+1)/2)! + ...

1/A(x) = 1 - x - x^3/6 + x^6/720 + x^10/3628800 - x^15/1307674368000 + ...

PROG

(PARI) {a(n) = my(A=1/sum(m=0, sqrtint(2*n+1), (-x)^(m*(m+1)/2)/(m*(m+1)/2)!+x*O(x^n))); n!*polcoeff(A, n)}