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A292119 O.g.f. equals the square of the e.g.f. of A291561. 1
1, 10, 130, 2100, 40950, 943740, 25269300, 774635400, 26836251750, 1038607069500, 44448725821500, 2084869401615000, 106355178306877500, 5861473946222895000, 346999395775257225000, 21956626245257906202000, 1478562610889805715023750, 105561794005139231136877500, 7963731010308915234880987500, 632966979266333111428303275000, 52862553418201438508049805852500 (list; graph; refs; listen; history; text; internal format)
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: A067313 A104130 A051607 * A113386 A302615 A281395

Adjacent sequences:  A292116 A292117 A292118 * A292120 A292121 A292122

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 18 2017

STATUS

approved

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Last modified August 20 06:04 EDT 2019. Contains 326139 sequences. (Running on oeis4.)