A292119 O.g.f. equals the square of the e.g.f. of A291561.

1, 10, 130, 2100, 40950, 943740, 25269300, 774635400, 26836251750, 1038607069500, 44448725821500, 2084869401615000, 106355178306877500, 5861473946222895000, 346999395775257225000, 21956626245257906202000, 1478562610889805715023750, 105561794005139231136877500, 7963731010308915234880987500, 632966979266333111428303275000, 52862553418201438508049805852500

Offset

2,2

Comments

A291561 is a diagonal in triangle A291560: a(n) = -A291560(n+1, n) for n >= 1; the e.g.f. of triangle A291560 equals arcsin( k*sin(x) ).

Links

Table of n, a(n) for n=2..22.

Example

O.g.f.: A(x) = x^2 + 10*x^3 + 130*x^4 + 2100*x^5 + 40950*x^6 + 943740*x^7 + 25269300*x^8 + 774635400*x^9 + 26836251750*x^10 + 1038607069500*x^11 + 44448725821500*x^12 + 2084869401615000*x^13 + 106355178306877500*x^14 + 5861473946222895000*x^15 + 346999395775257225000*x^16 + 21956626245257906202000*x^17 + 1478562610889805715023750*x^18 + ...
such that the square root of the g.f. equals the e.g.f. of A291561, which begins:
A(x)^(1/2) = x + 10*x^2/2! + 315*x^3/3! + 18900*x^4/4! + 1819125*x^5/5! + 255405150*x^6/6! + 49165491375*x^7/7! + 12417798393000*x^8/8! + 3981456609755625*x^9/9! + 1579311121869731250*x^10/10! + ... + A291561(n)*x^n/n! + ...

Prog

(PARI) {A291560(n, r) = (2*n-1)! * polcoeff( polcoeff( asin( k*sin(x + O(x^(2*n)))), 2*n-1, x), 2*r-1, k)}
{a(n) = polcoeff( sum(m=1, n, -A291560(m+1, m) * x^m / m! +x*O(x^n) )^2, n)}
for(n=2, 25, print1(a(n), ", "))

Crossrefs

Cf. A291561, A291560.

Sequence in context: A327810 A355422 A051607 * A113386 A302615 A281395

Adjacent sequences: A292116 A292117 A292118 * A292120 A292121 A292122

Keyword

nonn

Author

Paul D. Hanna, Sep 18 2017

Status

approved