The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A221534

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A221534

E.g.f.: Sum_{n>=0} a(n) * (cos(n*x) - sin(n*x))^n * x^n/n! = 1 + x.
(history; published version)

#4 by Paul D. Hanna at Sat Jan 19 08:29:46 EST 2013

STATUS

editing

approved

#3 by Paul D. Hanna at Sat Jan 19 08:29:43 EST 2013

NAME

allocated for Paul D. Hanna

E.g.f.: Sum_{n>=0} a(n) * (cos(n*x) - sin(n*x))^n * x^n/n! = 1 + x.

DATA

1, 1, 2, 27, 968, 68865, 8252496, 1505652267, 390426582272, 136910626544673, 62531921536979200, 36122742294179711643, 25777397243775426776064, 22288717300246130379501921, 22978204666564567674247942144, 27861330789200983137890612877675

OFFSET

0,3

EXAMPLE

By definition, the coefficients a(n) satisfy:

1+x = 1 + 1*(cos(x)-sin(x))*x + 2*(cos(2*x)-sin(2*x))^2*x^2/2! + 27*(cos(3*x)-sin(3*x))^3*x^3/3! + 968*(cos(4*x)-sin(4*x))^4*x^4/4! + 68865*(cos(5*x)-sin(5*x))^5*x^5/5! +...+ a(n)*(cos(n*x)-sin(n*x))^n*x^n/n! +...

PROG

(PARI) {a(n)=local(A=[1, 1], N); for(i=1, n, A=concat(A, 0); N=#A; A[N]=(N-1)!*(-Vec(sum(m=0, N-1, A[m+1]*x^m/m!*(cos(m*x+x*O(x^N))-sin(m*x+x*O(x^N)))^m))[N])); A[n+1]}

for(n=0, 25, print1(a(n), ", "))

CROSSREFS

Cf. A218798, A221535.

KEYWORD

allocated

nonn

AUTHOR

Paul D. Hanna, Jan 19 2013

STATUS

approved

editing

#2 by Paul D. Hanna at Sat Jan 19 08:25:12 EST 2013

KEYWORD

allocating

allocated

#1 by Paul D. Hanna at Sat Jan 19 08:25:12 EST 2013

NAME

allocated for Paul D. Hanna

KEYWORD

allocating

STATUS

approved