A381480 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x) * cos(x * A(x)) )^2.

1, 2, 14, 174, 3168, 76450, 2304720, 83473726, 3533382272, 171254814210, 9355068840960, 568799458870478, 38102773549750272, 2788540163472852386, 221380225364522119168, 18950242574522637197790, 1739955233454599038402560, 170582215179135413189856514, 17785491645892269582026145792

Offset

0,2

Comments

As stated in the comment of A185951, A185951(n,0) = 0^n.

Links

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381479.

a(n) = 2 * Sum_{k=0..n} k! * binomial(2*n+k+2,k)/(2*n+k+2) * i^(n-k) * A185951(n,k), where i is the imaginary unit.

E.g.f.: (1/x) * Series_Reversion( x*(1 - x*cos(x))^2 ).

Prog

(PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = 2*sum(k=0, n, k!*binomial(2*n+k+2, k)/(2*n+k+2)*I^(n-k)*a185951(n, k));

Crossrefs

Cf. A185951, A381478.

Sequence in context: A308449 A233224 A167014 * A370909 A377553 A379576

Adjacent sequences: A381477 A381478 A381479 * A381485 A381486 A381487

Keyword

nonn

Author

Seiichi Manyama, Feb 24 2025

Status

approved