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A187540 Binomial partial sums of the central Lah numbers. 11
1, 3, 41, 1315, 63825, 4116611, 331127353, 31915763811, 3585520583585, 460054836028675, 66377105303195721, 10637410917472061603, 1874707445757653437681, 360356280811211873453955, 75028021167256736753934425 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

Formula: a(n) = 1+sum(binomial(n,k)binomial(2k-1,k-1)(2k)!/k!,k=0..n).

Recurrence: for n>=3,  a(n) = 1/n*(-2 +(32 - 48*n + 16*n^2)*a(n-3) + (-31 + 63*n - 32*n^2)*a(n-2) + (3 - 14*n + 16*n^2)*a(n-1) )

E.g.f.: exp(x) (1/2 + 1/Pi K(16x) ), where K(z) is the elliptic integral of the first kind (defined as in Mathematica).

a(n) ~ 16^n*n^(n-1/2)*exp(1/16-n)/sqrt(2*Pi). - Vaclav Kotesovec, Aug 09 2013

MAPLE

seq(1+add(binomial(n, k)*binomial(2*k-1, k-1)*(2*k)!/k!, k=1..n), n=0..20);

MATHEMATICA

Table[1 + Sum[Binomial[n, k]Binomial[2k-1, k-1](2k)!/k!, {k, 1, n}], {n, 0, 20}]

PROG

(Maxima) makelist(1+sum(binomial(n, k)*binomial(2*k-1, k-1)*(2*k)!/k!, k, 1, n), n, 0, 12);

(PARI) a(n) = 1+sum(k=0, n, binomial(n, k)*binomial(2*k-1, k-1)*(2*k)!/k!) \\ Charles R Greathouse IV, Feb 07 2017

CROSSREFS

Cf. A187536, A008297, A111596, A187538, A187539, A187542, A187543, A187544, A187545, A187546, A187547, A187548.

Sequence in context: A012035 A012016 A207993 * A012104 A012147 A012011

Adjacent sequences:  A187537 A187538 A187539 * A187541 A187542 A187543

KEYWORD

nonn,easy,nice

AUTHOR

Emanuele Munarini, Mar 11 2011

STATUS

approved

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Last modified September 17 18:29 EDT 2021. Contains 347489 sequences. (Running on oeis4.)