A090364 Convolution of this sequence with its binomial transform equals the second iteration of the binomial transform upon this sequence.

1, 1, 3, 13, 79, 633, 6363, 77301, 1102791, 18070705, 334337203, 6890754093, 156506187679, 3882859101289, 104459523189387, 3028574143010661, 94129826448658551, 3121967981131094049, 110053554178639814499

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

G.f.: A(x) = A(x/(1-2x))/A(x/(1-x))*(1-x)/(1-2x).

a(n) ~ (n-1)! / (sqrt(5) * phi * log(phi)^(n+1)), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, May 28 2025

Mathematica

terms = 25; A[_] = 1; Do[A[x_] = A[x/(1-2*x)]/A[x/(1-x)]*(1-x)/(1-2*x) + O[x]^j // Normal, {j, 1, terms}]; CoefficientList[A[x], x] (* Vaclav Kotesovec, May 28 2025 *)

Prog

(PARI) {a(n)=local(A); if(n<0, 0, A=1+x+x*O(x^n); for(k=1, n, B=subst(A, x, x/(1-x))/(1-x)+x*O(x^n); C=subst(B, x, x/(1-x))/(1-x)+x*O(x^n); A=A-A*B+C); polcoeff(A, n, x))}

Crossrefs

Sequence in context: A261601 A125659 A010844 * A112935 A258377 A335636

Adjacent sequences: A090361 A090362 A090363 * A090365 A090366 A090367

Keyword

nonn

Author

Paul D. Hanna, Nov 26 2003

Status

approved