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A264149 Denominators of rational coefficients related to Stirling's asymptotic series for the Gamma function. 2
1, 3, 12, 135, 288, 2835, 51840, 8505, 2488320, 12629925, 209018880, 492567075, 75246796800, 1477701225, 902961561600, 39565450299375, 86684309913600, 2255230667064375, 514904800886784000, 6765692001193125, 86504006548979712000, 7002491221234884375 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 20 14:02 EST 2020. Contains 331094 sequences. (Running on oeis4.)