A093523 Inverse binomial transform of A010054 (1 if triangular number else 0).

1, 0, -1, 3, -7, 14, -24, 34, -35, 8, 82, -298, 759, -1704, 3627, -7538, 15425, -30992, 60673, -114647, 206853, -351365, 549132, -752653, 784277, -162126, -2252600, 8950526, -25129652, 61349528, -138789534, 299803944, -629297799, 1298075184, -2650139349, 5375982063, -10849417306

Offset

0,4

Comments

The e.g.f., F(x) = exp(-x)*sum_{n>=0} x^(n*(n+1)/2)/(n*(n+1)/2)!, is approximated by 1/sqrt(2x) for x>1; example: F(1)=0.79758, F(2)=0.59852, F(10)=0.23183, F(50)=0.10063.

Links

Table of n, a(n) for n=0..36.

Formula

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

Mathematica

Table[Sum[(-1)^(n-k) * Binomial[n, k] * SquaresR[1, 8*k+1]/2, {k, 0, n}], {n, 0, 40}] (* Vaclav Kotesovec, Oct 31 2017 *)

Prog

(PARI) {a(n)=n!*polcoeff((sum(k=0, sqrtint(2*n+1), x^(k*(k+1)/2)/(k*(k+1)/2)!)*sum(j=0, n, (-x)^j/j!)+x*O(x^n)), n)}

Crossrefs

Sequence in context: A140462 A227841 A225256 * A173247 A123386 A060999

Adjacent sequences: A093520 A093521 A093522 * A093524 A093525 A093526

Keyword

sign

Author

Paul D. Hanna, Mar 30 2004

Status

approved