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A117397 Column 3 of triangle A117396. 1
1, 4, 19, 109, 739, 5779, 51139, 504739, 5494339, 65369539, 843747139, 11741033539, 175200329539, 2790549065539, 47251477577539, 847548190793539, 16053185741897539, 320165936763977539, 6706533708227657539, 147206624680428617539, 3378708717041050697539 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Equals the partial sums of column 3 of triangle A092582.

LINKS

Table of n, a(n) for n=0..20.

FORMULA

G.f. satisfies A(x) = (1-x)/(1 - 5*x + 5*x^2) * (1 + x^2*A'(x)).

a(n) = 1 + Sum_{k=4..n+3} k!*3/4! for n > 0, with a(0)=1.

G.f.: W(0)/(8*x*(1-x)) -1/(4*x), where W(k) = 1 + 1/( 1 - x*(k+3)/( x*(k+3) + 1/W(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Aug 20 2013

G.f.: (Sum_{n>=0} (n+2)!*x^n)/(8*x*(1-x)) - 1/(4*x). - Sergei N. Gladkovskii, Aug 20 2013

EXAMPLE

G.f.: A(x) = 1 + 4*x + 19*x^2 + 109*x^3 + 739*x^4 + 5779*x^5 + 51139*x^6 + 504739*x^7 + 5494339*x^8 + 65369539*x^9 + 843747139*x^10 + ...

MAPLE

a:=n->sum(j!/8, j=2..n): seq(a(n), n=3..21); # Zerinvary Lajos, Jan 08 2007

MATHEMATICA

Table[Sum[i!/8, {i, 2, n}], {n, 3, 21}] (* Zerinvary Lajos, Jul 12 2009 *)

PROG

(PARI) {a(n)=1+sum(k=4, n+3, k!)*3/4!}

for(n=0, 25, print1(a(n), ", "))

CROSSREFS

Cf. A117396 (triangle), A014288 (column 1), A056199 (column 2), A003422 (row sums); A092582.

Sequence in context: A306183 A241840 A199318 * A004212 A243241 A060905

Adjacent sequences:  A117394 A117395 A117396 * A117398 A117399 A117400

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Mar 11 2006

STATUS

approved

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Last modified June 13 22:55 EDT 2021. Contains 345016 sequences. (Running on oeis4.)