A264149 Denominators of rational coefficients related to Stirling's asymptotic series for the Gamma function.

1, 3, 12, 135, 288, 2835, 51840, 8505, 2488320, 12629925, 209018880, 492567075, 75246796800, 1477701225, 902961561600, 39565450299375, 86684309913600, 2255230667064375, 514904800886784000, 6765692001193125, 86504006548979712000, 7002491221234884375

Offset

0,2

Comments

See A264148 for definitions and cross-references.

Links

G. C. Greubel, Table of n, a(n) for n = 0..589

Maple

h := proc(k) option remember; local j; `if`(k<=0, 1,
(h(k-1)/k-add((h(k-j)*h(j))/(j+1), j=1..k-1))/(1+1/(k+1))) end:
SGGS := n -> h(n)*doublefactorial(n-1):
A264149 := n -> denom(SGGS(n));
seq(A264149(n), n=0..26);

Mathematica

h[k_]:= h[k] = If[k <= 0, 1, (h[k - 1]/k - Sum[h[k - j]*h[j]/(j + 1), {j, 1, k - 1}])/(1 + 1/(k + 1))]; a[n_]:= h[n]*Factorial2[n - 1] // Denominator; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Feb 09 2018 *)

Prog

(Sage)
def A264149(n):
    @cached_function
    def h(k):
        if k<=0: return 1
        S = sum((h(k-j)*h(j))/(j+1) for j in (1..k-1))
        return (h(k-1)/k-S)/(1+1/(k+1))
    return denominator(h(n)*(n-1).multifactorial(2))
print([A264149(n) for n in (0..21)])

Crossrefs

Cf. numerators in A264148.

Sequence in context: A138392 A152544 A280115 * A035087 A056426 A056417

Adjacent sequences: A264146 A264147 A264148 * A264150 A264151 A264152

Keyword

nonn,frac

Author

Peter Luschny, Nov 05 2015

Status

approved