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A082580 A sum of Lah numbers and binomial coefficients. 1
1, 2, 10, 68, 574, 5732, 65724, 847800, 12120966, 189890588, 3230531356, 59246895512, 1164225730540, 24387062160008, 542155626123544, 12743158072837680, 315624979700257350, 8213507146488950700 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..17.

FORMULA

Formula: a(n) = Sum[ Lah[ n, k ] binomial[ 2 k, k ], { k, 0, n } ] where Lah[n, k] = binomial[ n - 1, k - 1 ] n! / k! are the Lah numbers. Recurrence: ( n + 3 ) a(n+3) - ( 3 n^2 + 17 n + 24 ) a(n+2) + 3 ( n + 3 )( n + 2 )( n + 1 ) a(n+1) - ( n + 2 )( n + 1 )^2 n a(n) = 0

E.g.f.: BesselI(0, 2*x/(1-x))*exp(2*x/(1-x)). - Vladeta Jovovic, Sep 13 2003

a(n) ~ exp(4*sqrt(n) - n - 2) * n^(n - 1/2) / sqrt(2*Pi). - Vaclav Kotesovec, Jun 07 2019

MATHEMATICA

RecurrenceTable[{-(-3 + n) (-2 + n)^2 (-1 + n) a[-3 + n] + 3 (-2 + n) (-1 + n) n a[-2 + n] - n (-1 + 3 n) a[-1 + n] + n a[n] == 0, a[0] == 1, a[1] == 2, a[2] == 10}, a, {n, 0, 20}] (* Vaclav Kotesovec, Jun 07 2019 *)

CROSSREFS

Sequence in context: A074603 A110520 A136633 * A231492 A136658 A165968

Adjacent sequences:  A082577 A082578 A082579 * A082581 A082582 A082583

KEYWORD

easy,nonn

AUTHOR

Emanuele Munarini, May 07 2003

STATUS

approved

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Last modified October 22 18:17 EDT 2019. Contains 328319 sequences. (Running on oeis4.)